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Theorem nchoicelem16 6304

Description: Lemma for nchoice 6308. Set up stratification for nchoicelem17 6305. (Contributed by SF, 19-Mar-2015.)

Assertion

Ref	Expression
nchoicelem16	c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c

Distinct variable group:   ,

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Proof of Theorem nchoicelem16 Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		unab 3521	. . 3 c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
2		elima3 4756	. . . . . 6 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC 1c AddC
3		vex 2862	. . . . . . . . . . 11
4	3	eluni1 4173	. . . . . . . . . 10 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
5		snex 4111	. . . . . . . . . . 11
6	5	elcompl 3225	. . . . . . . . . 10 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
7		elimapw13 4946	. . . . . . . . . . . 12 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC NC SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c
8		spacval 6282	. . . . . . . . . . . . . . . . . 18 NC Spac Clos1 NC NC 2c ↑c
9	8	nceqd 6110	. . . . . . . . . . . . . . . . 17 NC Nc Spac Nc Clos1 NC NC 2c ↑c
10	9	eqeq1d 2361	. . . . . . . . . . . . . . . 16 NC Nc Spac Nc Clos1 NC NC 2c ↑c
11		tccl 6160	. . . . . . . . . . . . . . . . . . . 20 NC Tc NC
12		spacval 6282	. . . . . . . . . . . . . . . . . . . 20 Tc NC Spac Tc Clos1 Tc NC NC 2c ↑c
13	11, 12	syl 15	. . . . . . . . . . . . . . . . . . 19 NC Spac Tc Clos1 Tc NC NC 2c ↑c
14	13	eleq1d 2419	. . . . . . . . . . . . . . . . . 18 NC Spac Tc Fin Clos1 Tc NC NC 2c ↑c Fin
15	13	nceqd 6110	. . . . . . . . . . . . . . . . . . . 20 NC Nc Spac Tc Nc Clos1 Tc NC NC 2c ↑c
16	15	eqeq1d 2361	. . . . . . . . . . . . . . . . . . 19 NC Nc Spac Tc Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 1c
17	15	eqeq1d 2361	. . . . . . . . . . . . . . . . . . 19 NC Nc Spac Tc Tc 2c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
18	16, 17	orbi12d 690	. . . . . . . . . . . . . . . . . 18 NC Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
19	14, 18	anbi12d 691	. . . . . . . . . . . . . . . . 17 NC Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
20	19	notbid 285	. . . . . . . . . . . . . . . 16 NC Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
21	10, 20	anbi12d 691	. . . . . . . . . . . . . . 15 NC Nc Spac Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c Nc Clos1 NC NC 2c ↑c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
22		eldif 3221	. . . . . . . . . . . . . . . 16 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c
23		snex 4111	. . . . . . . . . . . . . . . . . . . 20
24	23, 3	opsnelsi 5774	. . . . . . . . . . . . . . . . . . 19 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
25		opelcnv 4893	. . . . . . . . . . . . . . . . . . 19 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
26		opelres 4950	. . . . . . . . . . . . . . . . . . . 20 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
27		opelcnv 4893	. . . . . . . . . . . . . . . . . . . . . 22 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
28		opelco 4884	. . . . . . . . . . . . . . . . . . . . . . 23 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
29		snex 4111	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28
30	29	brsnsi1 5775	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
31	30	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . 26 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
32		19.41v 1901	. . . . . . . . . . . . . . . . . . . . . . . . . 26 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
33	31, 32	bitr4i 243	. . . . . . . . . . . . . . . . . . . . . . . . 25 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
34	33	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . 24 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
35		excom 1741	. . . . . . . . . . . . . . . . . . . . . . . 24 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
36	34, 35	bitri 240	. . . . . . . . . . . . . . . . . . . . . . 23 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
37		anass 630	. . . . . . . . . . . . . . . . . . . . . . . . . 26 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
38	37	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . 25 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
39		snex 4111	. . . . . . . . . . . . . . . . . . . . . . . . . 26
40		breq1 4642	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 S S
41	40	anbi2d 684	. . . . . . . . . . . . . . . . . . . . . . . . . 26 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
42	39, 41	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . . . 25 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
43		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
44		df-br 4640	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
45		spacvallem1 6281	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 NC NC 2c ↑c
46	45, 29	nchoicelem10 6298	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
47	43, 44, 46	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . 26 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
48		vex 2862	. . . . . . . . . . . . . . . . . . . . . . . . . . 27
49	48, 3	brssetsn 4759	. . . . . . . . . . . . . . . . . . . . . . . . . 26 S
50	47, 49	anbi12i 678	. . . . . . . . . . . . . . . . . . . . . . . . 25 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
51	38, 42, 50	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . 24 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
52	51	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . 23 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
53	28, 36, 52	3bitri 262	. . . . . . . . . . . . . . . . . . . . . 22 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
54	29, 45	clos1ex 5876	. . . . . . . . . . . . . . . . . . . . . . 23 Clos1 NC NC 2c ↑c
55		eleq1 2413	. . . . . . . . . . . . . . . . . . . . . . 23 Clos1 NC NC 2c ↑c Clos1 NC NC 2c ↑c
56	54, 55	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . 22 Clos1 NC NC 2c ↑c Clos1 NC NC 2c ↑c
57	27, 53, 56	3bitri 262	. . . . . . . . . . . . . . . . . . . . 21 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
58	57	anbi1i 676	. . . . . . . . . . . . . . . . . . . 20 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Clos1 NC NC 2c ↑c NC
59		ancom 437	. . . . . . . . . . . . . . . . . . . 20 Clos1 NC NC 2c ↑c NC NC Clos1 NC NC 2c ↑c
60	26, 58, 59	3bitri 262	. . . . . . . . . . . . . . . . . . 19 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC NC Clos1 NC NC 2c ↑c
61	24, 25, 60	3bitri 262	. . . . . . . . . . . . . . . . . 18 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC NC Clos1 NC NC 2c ↑c
62		eqcom 2355	. . . . . . . . . . . . . . . . . . 19 Nc Clos1 NC NC 2c ↑c Nc Clos1 NC NC 2c ↑c
63	54	eqnc2 6129	. . . . . . . . . . . . . . . . . . 19 Nc Clos1 NC NC 2c ↑c NC Clos1 NC NC 2c ↑c
64	62, 63	bitri 240	. . . . . . . . . . . . . . . . . 18 Nc Clos1 NC NC 2c ↑c NC Clos1 NC NC 2c ↑c
65	61, 64	bitr4i 243	. . . . . . . . . . . . . . . . 17 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Nc Clos1 NC NC 2c ↑c
66		elimapw11c 4948	. . . . . . . . . . . . . . . . . . 19 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
67		oteltxp 5782	. . . . . . . . . . . . . . . . . . . . 21 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
68		snex 4111	. . . . . . . . . . . . . . . . . . . . . . . 24
69	68, 23	opsnelsi 5774	. . . . . . . . . . . . . . . . . . . . . . 23 SI SI TcFn SI TcFn
70		vex 2862	. . . . . . . . . . . . . . . . . . . . . . . . 25
71	70, 29	opsnelsi 5774	. . . . . . . . . . . . . . . . . . . . . . . 24 SI TcFn TcFn
72		df-br 4640	. . . . . . . . . . . . . . . . . . . . . . . 24 TcFn TcFn
73		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . 24 TcFn TcFn
74	71, 72, 73	3bitr2i 264	. . . . . . . . . . . . . . . . . . . . . . 23 SI TcFn TcFn
75		vex 2862	. . . . . . . . . . . . . . . . . . . . . . . 24
76	75	brtcfn 6246	. . . . . . . . . . . . . . . . . . . . . . 23 TcFn Tc
77	69, 74, 76	3bitri 262	. . . . . . . . . . . . . . . . . . . . . 22 SI SI TcFn Tc
78		opelco 4884	. . . . . . . . . . . . . . . . . . . . . . 23 TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC TcFn AddC 1c AddC 2c Nn
79		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . 26 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
80		brres 4949	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
81		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
82		brco 4883	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
83	68	brsnsi1 5775	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
84	83	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
85		19.41v 1901	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
86	84, 85	bitr4i 243	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
87	86	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
88		excom 1741	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
89		anass 630	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
90	89	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
91		snex 4111	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
92		breq1 4642	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 S S
93	92	anbi2d 684	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
94	91, 93	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S
95		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
96		df-br 4640	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
97	45, 68	nchoicelem10 6298	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
98	95, 96, 97	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
99		vex 2862	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
100	99, 48	brssetsn 4759	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 S
101	98, 100	anbi12i 678	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
102	90, 94, 101	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
103	102	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
104	87, 88, 103	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
105		df-clel 2349	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Clos1 NC NC 2c ↑c Clos1 NC NC 2c ↑c
106	104, 105	bitr4i 243	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c S Clos1 NC NC 2c ↑c
107	81, 82, 106	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c Clos1 NC NC 2c ↑c
108	107	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Clos1 NC NC 2c ↑c NC
109		ancom 437	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Clos1 NC NC 2c ↑c NC NC Clos1 NC NC 2c ↑c
110	80, 108, 109	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC NC Clos1 NC NC 2c ↑c
111	68, 45	clos1ex 5876	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Clos1 NC NC 2c ↑c
112	111	eqnc2 6129	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 Nc Clos1 NC NC 2c ↑c NC Clos1 NC NC 2c ↑c
113	110, 112	bitr4i 243	. . . . . . . . . . . . . . . . . . . . . . . . . 26 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Nc Clos1 NC NC 2c ↑c
114	79, 113	bitri 240	. . . . . . . . . . . . . . . . . . . . . . . . 25 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Nc Clos1 NC NC 2c ↑c
115		brres 4949	. . . . . . . . . . . . . . . . . . . . . . . . . 26 TcFn AddC 1c AddC 2c Nn TcFn AddC 1c AddC 2c Nn
116		brco 4883	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 TcFn AddC 1c AddC 2c AddC 1c AddC 2c TcFn
117		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 AddC 1c AddC 2c AddC 1c AddC 2c
118		brun 4692	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 AddC 1c AddC 2c AddC 1c AddC 2c
119		brco 4883	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 AddC 1c 1c AddC
120		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1c 1c
121		brres 4949	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1c 1c
122		eliniseg 5020	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 1c 1c
123	122	anbi2i 675	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1c 1c
124	121, 123	bitri 240	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1c 1c
125		1cex 4142	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 1c
126	99, 125	op1st2nd 5790	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 1c 1c
127	120, 124, 126	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1c 1c
128	127	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1c AddC 1c AddC
129	128	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1c AddC 1c AddC
130	99, 125	opex 4588	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1c
131		breq1 4642	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1c AddC 1c AddC
132	130, 131	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 1c AddC 1c AddC
133	119, 129, 132	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 AddC 1c 1c AddC
134	99, 125	braddcfn 5826	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1c AddC 1c
135		eqcom 2355	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 1c 1c
136	133, 134, 135	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 AddC 1c 1c
137		brco 4883	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 AddC 2c 2c AddC
138		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2c 2c
139		brres 4949	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2c 2c
140		eliniseg 5020	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2c 2c
141	140	anbi2i 675	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2c 2c
142	139, 141	bitri 240	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2c 2c
143		2nc 6168	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2c NC
144	143	elexi 2868	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2c
145	99, 144	op1st2nd 5790	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2c 2c
146	138, 142, 145	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2c 2c
147	146	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2c AddC 2c AddC
148	147	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2c AddC 2c AddC
149	99, 144	opex 4588	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2c
150		breq1 4642	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2c AddC 2c AddC
151	149, 150	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2c AddC 2c AddC
152	137, 148, 151	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 AddC 2c 2c AddC
153	99, 144	braddcfn 5826	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2c AddC 2c
154		eqcom 2355	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2c 2c
155	152, 153, 154	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 AddC 2c 2c
156	136, 155	orbi12i 507	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 AddC 1c AddC 2c 1c 2c
157	117, 118, 156	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 AddC 1c AddC 2c 1c 2c
158		brcnv 4892	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 TcFn TcFn
159	3	brtcfn 6246	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 TcFn Tc
160	158, 159	bitri 240	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 TcFn Tc
161	157, 160	anbi12i 678	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 AddC 1c AddC 2c TcFn 1c 2c Tc
162		ancom 437	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 1c 2c Tc Tc 1c 2c
163	161, 162	bitri 240	. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 AddC 1c AddC 2c TcFn Tc 1c 2c
164	163	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 AddC 1c AddC 2c TcFn Tc 1c 2c
165		tcex 6157	. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Tc
166		addceq1 4383	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Tc 1c Tc 1c
167	166	eqeq2d 2364	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Tc 1c Tc 1c
168		addceq1 4383	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Tc 2c Tc 2c
169	168	eqeq2d 2364	. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Tc 2c Tc 2c
170	167, 169	orbi12d 690	. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Tc 1c 2c Tc 1c Tc 2c
171	165, 170	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Tc 1c 2c Tc 1c Tc 2c
172	116, 164, 171	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . . . 27 TcFn AddC 1c AddC 2c Tc 1c Tc 2c
173	172	anbi1i 676	. . . . . . . . . . . . . . . . . . . . . . . . . 26 TcFn AddC 1c AddC 2c Nn Tc 1c Tc 2c Nn
174		ancom 437	. . . . . . . . . . . . . . . . . . . . . . . . . 26 Tc 1c Tc 2c Nn Nn Tc 1c Tc 2c
175	115, 173, 174	3bitri 262	. . . . . . . . . . . . . . . . . . . . . . . . 25 TcFn AddC 1c AddC 2c Nn Nn Tc 1c Tc 2c
176	114, 175	anbi12i 678	. . . . . . . . . . . . . . . . . . . . . . . 24 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC TcFn AddC 1c AddC 2c Nn Nc Clos1 NC NC 2c ↑c Nn Tc 1c Tc 2c
177	176	exbii 1582	. . . . . . . . . . . . . . . . . . . . . . 23 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC TcFn AddC 1c AddC 2c Nn Nc Clos1 NC NC 2c ↑c Nn Tc 1c Tc 2c
178		ncex 6117	. . . . . . . . . . . . . . . . . . . . . . . 24 Nc Clos1 NC NC 2c ↑c
179		eleq1 2413	. . . . . . . . . . . . . . . . . . . . . . . . . 26 Nc Clos1 NC NC 2c ↑c Nn Nc Clos1 NC NC 2c ↑c Nn
180		finnc 6243	. . . . . . . . . . . . . . . . . . . . . . . . . 26 Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Nn
181	179, 180	syl6bbr 254	. . . . . . . . . . . . . . . . . . . . . . . . 25 Nc Clos1 NC NC 2c ↑c Nn Clos1 NC NC 2c ↑c Fin
182		eqeq1 2359	. . . . . . . . . . . . . . . . . . . . . . . . . 26 Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 1c
183		eqeq1 2359	. . . . . . . . . . . . . . . . . . . . . . . . . 26 Nc Clos1 NC NC 2c ↑c Tc 2c Nc Clos1 NC NC 2c ↑c Tc 2c
184	182, 183	orbi12d 690	. . . . . . . . . . . . . . . . . . . . . . . . 25 Nc Clos1 NC NC 2c ↑c Tc 1c Tc 2c Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
185	181, 184	anbi12d 691	. . . . . . . . . . . . . . . . . . . . . . . 24 Nc Clos1 NC NC 2c ↑c Nn Tc 1c Tc 2c Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
186	178, 185	ceqsexv 2894	. . . . . . . . . . . . . . . . . . . . . . 23 Nc Clos1 NC NC 2c ↑c Nn Tc 1c Tc 2c Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
187	78, 177, 186	3bitri 262	. . . . . . . . . . . . . . . . . . . . . 22 TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
188	77, 187	anbi12i 678	. . . . . . . . . . . . . . . . . . . . 21 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Tc Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
189	67, 188	bitri 240	. . . . . . . . . . . . . . . . . . . 20 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Tc Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
190	189	exbii 1582	. . . . . . . . . . . . . . . . . . 19 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC Tc Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c
191		tcex 6157	. . . . . . . . . . . . . . . . . . . 20 Tc
192		sneq 3744	. . . . . . . . . . . . . . . . . . . . . . 23 Tc Tc
193		clos1eq1 5874	. . . . . . . . . . . . . . . . . . . . . . 23 Tc Clos1 NC NC 2c ↑c Clos1 Tc NC NC 2c ↑c
194	192, 193	syl 15	. . . . . . . . . . . . . . . . . . . . . 22 Tc Clos1 NC NC 2c ↑c Clos1 Tc NC NC 2c ↑c
195	194	eleq1d 2419	. . . . . . . . . . . . . . . . . . . . 21 Tc Clos1 NC NC 2c ↑c Fin Clos1 Tc NC NC 2c ↑c Fin
196	194	nceqd 6110	. . . . . . . . . . . . . . . . . . . . . . 23 Tc Nc Clos1 NC NC 2c ↑c Nc Clos1 Tc NC NC 2c ↑c
197	196	eqeq1d 2361	. . . . . . . . . . . . . . . . . . . . . 22 Tc Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 1c
198	196	eqeq1d 2361	. . . . . . . . . . . . . . . . . . . . . 22 Tc Nc Clos1 NC NC 2c ↑c Tc 2c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
199	197, 198	orbi12d 690	. . . . . . . . . . . . . . . . . . . . 21 Tc Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
200	195, 199	anbi12d 691	. . . . . . . . . . . . . . . . . . . 20 Tc Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
201	191, 200	ceqsexv 2894	. . . . . . . . . . . . . . . . . . 19 Tc Clos1 NC NC 2c ↑c Fin Nc Clos1 NC NC 2c ↑c Tc 1c Nc Clos1 NC NC 2c ↑c Tc 2c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
202	66, 190, 201	3bitri 262	. . . . . . . . . . . . . . . . . 18 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
203	202	notbii 287	. . . . . . . . . . . . . . . . 17 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
204	65, 203	anbi12i 678	. . . . . . . . . . . . . . . 16 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Nc Clos1 NC NC 2c ↑c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
205	22, 204	bitri 240	. . . . . . . . . . . . . . 15 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Nc Clos1 NC NC 2c ↑c Clos1 Tc NC NC 2c ↑c Fin Nc Clos1 Tc NC NC 2c ↑c Tc 1c Nc Clos1 Tc NC NC 2c ↑c Tc 2c
206	21, 205	syl6rbbr 255	. . . . . . . . . . . . . 14 NC SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Nc Spac Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c
207		tceq 6158	. . . . . . . . . . . . . . . . . . . 20 Nc Spac Tc Nc Spac Tc
208	207	addceq1d 4389	. . . . . . . . . . . . . . . . . . 19 Nc Spac Tc Nc Spac 1c Tc 1c
209	208	eqeq2d 2364	. . . . . . . . . . . . . . . . . 18 Nc Spac Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc 1c
210	207	addceq1d 4389	. . . . . . . . . . . . . . . . . . 19 Nc Spac Tc Nc Spac 2c Tc 2c
211	210	eqeq2d 2364	. . . . . . . . . . . . . . . . . 18 Nc Spac Nc Spac Tc Tc Nc Spac 2c Nc Spac Tc Tc 2c
212	209, 211	orbi12d 690	. . . . . . . . . . . . . . . . 17 Nc Spac Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c
213	212	anbi2d 684	. . . . . . . . . . . . . . . 16 Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c
214	213	notbid 285	. . . . . . . . . . . . . . 15 Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c
215	214	pm5.32i 618	. . . . . . . . . . . . . 14 Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c Nc Spac Spac Tc Fin Nc Spac Tc Tc 1c Nc Spac Tc Tc 2c
216	206, 215	syl6bbr 254	. . . . . . . . . . . . 13 NC SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
217	216	rexbiia 2647	. . . . . . . . . . . 12 NC SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
218		rexanali 2660	. . . . . . . . . . . 12 NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
219	7, 217, 218	3bitrri 263	. . . . . . . . . . 11 NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
220	219	con1bii 321	. . . . . . . . . 10 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
221	4, 6, 220	3bitri 262	. . . . . . . . 9 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
222		opelco 4884	. . . . . . . . . . 11 1c AddC AddC 1c
223		brcnv 4892	. . . . . . . . . . . . . 14 AddC AddC
224		brres 4949	. . . . . . . . . . . . . . 15 1c 1c
225		eliniseg 5020	. . . . . . . . . . . . . . . . 17 1c 1c
226	225	anbi2i 675	. . . . . . . . . . . . . . . 16 1c 1c
227		ancom 437	. . . . . . . . . . . . . . . 16 1c 1c
228	226, 227	bitri 240	. . . . . . . . . . . . . . 15 1c 1c
229	125, 99	op1st2nd 5790	. . . . . . . . . . . . . . 15 1c 1c
230	224, 228, 229	3bitri 262	. . . . . . . . . . . . . 14 1c 1c
231	223, 230	anbi12i 678	. . . . . . . . . . . . 13 AddC 1c AddC 1c
232		ancom 437	. . . . . . . . . . . . 13 AddC 1c 1c AddC
233	231, 232	bitri 240	. . . . . . . . . . . 12 AddC 1c 1c AddC
234	233	exbii 1582	. . . . . . . . . . 11 AddC 1c 1c AddC
235	125, 99	opex 4588	. . . . . . . . . . . 12 1c
236		breq1 4642	. . . . . . . . . . . 12 1c AddC 1c AddC
237	235, 236	ceqsexv 2894	. . . . . . . . . . 11 1c AddC 1c AddC
238	222, 234, 237	3bitri 262	. . . . . . . . . 10 1c AddC 1c AddC
239	125, 99	braddcfn 5826	. . . . . . . . . 10 1c AddC 1c
240		eqcom 2355	. . . . . . . . . 10 1c 1c
241	238, 239, 240	3bitri 262	. . . . . . . . 9 1c AddC 1c
242	221, 241	anbi12i 678	. . . . . . . 8 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC 1c AddC NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c 1c
243		ancom 437	. . . . . . . 8 NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c 1c 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
244	242, 243	bitri 240	. . . . . . 7 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC 1c AddC 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
245	244	exbii 1582	. . . . . 6 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC 1c AddC 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
246	125, 99	addcex 4394	. . . . . . 7 1c
247		eqeq2 2362	. . . . . . . . 9 1c Nc Spac Nc Spac 1c
248	247	imbi1d 308	. . . . . . . 8 1c Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
249	248	ralbidv 2634	. . . . . . 7 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
250	246, 249	ceqsexv 2894	. . . . . 6 1c NC Nc Spac Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
251	2, 245, 250	3bitri 262	. . . . 5 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
252	251	abbi2i 2464	. . . 4 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
253	252	uneq2i 3415	. . 3 c We NC 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
254		imor 401	. . . 4 c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
255	254	abbii 2465	. . 3 c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
256	1, 253, 255	3eqtr4i 2383	. 2 c We NC 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c
257		abexv 4324	. . 3 c We NC
258		2ndex 5112	. . . . . 6
259		1stex 4739	. . . . . . . 8
260	259	cnvex 5102	. . . . . . 7
261		snex 4111	. . . . . . 7 1c
262	260, 261	imaex 4747	. . . . . 6 1c
263	258, 262	resex 5117	. . . . 5 1c
264		addcfnex 5824	. . . . . 6 AddC
265	264	cnvex 5102	. . . . 5 AddC
266	263, 265	coex 4750	. . . 4 1c AddC
267		ssetex 4744	. . . . . . . . . . . . 13 S
268	267	ins3ex 5798	. . . . . . . . . . . . . . . . . 18 Ins3 S
269	267	complex 4104	. . . . . . . . . . . . . . . . . . . . . . 23 ∼ S
270	269	cnvex 5102	. . . . . . . . . . . . . . . . . . . . . 22 ∼ S
271	267	cnvex 5102	. . . . . . . . . . . . . . . . . . . . . . 23 S
272	45	imageex 5801	. . . . . . . . . . . . . . . . . . . . . . . . 25 Image NC NC 2c ↑c
273	267, 272	coex 4750	. . . . . . . . . . . . . . . . . . . . . . . 24 S Image NC NC 2c ↑c
274	273	fixex 5789	. . . . . . . . . . . . . . . . . . . . . . 23 S Image NC NC 2c ↑c
275	271, 274	resex 5117	. . . . . . . . . . . . . . . . . . . . . 22 S S Image NC NC 2c ↑c
276	270, 275	txpex 5785	. . . . . . . . . . . . . . . . . . . . 21 ∼ S S S Image NC NC 2c ↑c
277	276	rnex 5107	. . . . . . . . . . . . . . . . . . . 20 ∼ S S S Image NC NC 2c ↑c
278	277	complex 4104	. . . . . . . . . . . . . . . . . . 19 ∼ ∼ S S S Image NC NC 2c ↑c
279	278	ins2ex 5797	. . . . . . . . . . . . . . . . . 18 Ins2 ∼ ∼ S S S Image NC NC 2c ↑c
280	268, 279	symdifex 4108	. . . . . . . . . . . . . . . . 17 Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c
281	280, 125	imaex 4747	. . . . . . . . . . . . . . . 16 Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
282	281	complex 4104	. . . . . . . . . . . . . . 15 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
283	282	cnvex 5102	. . . . . . . . . . . . . 14 ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
284	283	siex 4753	. . . . . . . . . . . . 13 SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
285	267, 284	coex 4750	. . . . . . . . . . . 12 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
286	285	cnvex 5102	. . . . . . . . . . 11 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c
287		ncsex 6111	. . . . . . . . . . 11 NC
288	286, 287	resex 5117	. . . . . . . . . 10 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
289	288	cnvex 5102	. . . . . . . . 9 S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
290	289	siex 4753	. . . . . . . 8 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
291		tcfnex 6244	. . . . . . . . . . . . 13 TcFn
292	291	cnvex 5102	. . . . . . . . . . . 12 TcFn
293	292	siex 4753	. . . . . . . . . . 11 SI TcFn
294	293	siex 4753	. . . . . . . . . 10 SI SI TcFn
295	258	cnvex 5102	. . . . . . . . . . . . . . . . . . 19
296	295, 261	imaex 4747	. . . . . . . . . . . . . . . . . 18 1c
297	259, 296	resex 5117	. . . . . . . . . . . . . . . . 17 1c
298	297	cnvex 5102	. . . . . . . . . . . . . . . 16 1c
299	264, 298	coex 4750	. . . . . . . . . . . . . . 15 AddC 1c
300		snex 4111	. . . . . . . . . . . . . . . . . . 19 2c
301	295, 300	imaex 4747	. . . . . . . . . . . . . . . . . 18 2c
302	259, 301	resex 5117	. . . . . . . . . . . . . . . . 17 2c
303	302	cnvex 5102	. . . . . . . . . . . . . . . 16 2c
304	264, 303	coex 4750	. . . . . . . . . . . . . . 15 AddC 2c
305	299, 304	unex 4106	. . . . . . . . . . . . . 14 AddC 1c AddC 2c
306	305	cnvex 5102	. . . . . . . . . . . . 13 AddC 1c AddC 2c
307	292, 306	coex 4750	. . . . . . . . . . . 12 TcFn AddC 1c AddC 2c
308		nncex 4396	. . . . . . . . . . . 12 Nn
309	307, 308	resex 5117	. . . . . . . . . . 11 TcFn AddC 1c AddC 2c Nn
310	309, 289	coex 4750	. . . . . . . . . 10 TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
311	294, 310	txpex 5785	. . . . . . . . 9 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC
312	125	pw1ex 4303	. . . . . . . . 9 1 1c
313	311, 312	imaex 4747	. . . . . . . 8 SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c
314	290, 313	difex 4107	. . . . . . 7 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c
315	287	pw1ex 4303	. . . . . . . . 9 1 NC
316	315	pw1ex 4303	. . . . . . . 8 1 1 NC
317	316	pw1ex 4303	. . . . . . 7 1 1 1 NC
318	314, 317	imaex 4747	. . . . . 6 SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
319	318	complex 4104	. . . . 5 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
320	319	uni1ex 4293	. . . 4 ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
321	266, 320	imaex 4747	. . 3 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
322	257, 321	unex 4106	. 2 c We NC 1c AddC ⋃1 ∼ SI S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC SI SI TcFn TcFn AddC 1c AddC 2c Nn S SI ∼ Ins3 S Ins2 ∼ ∼ S S S Image NC NC 2c ↑c 1c NC 1 1c1 1 1 NC
323	256, 322	eqeltrri 2424	1 c We NC NC Nc Spac 1c Spac Tc Fin Nc Spac Tc Tc Nc Spac 1c Nc Spac Tc Tc Nc Spac 2c

Colors of variables: wff setvar class

Syntax hints:   wn 3   wi 4   wo 357   wa 358   w3a 934  wex 1541   wceq 1642   wcel 1710  cab 2339  wral 2614  wrex 2615  cvv 2859   ∼ ccompl 3205   cdif 3206   cun 3207   csymdif 3209  csn 3737  ⋃1cuni1 4133  1cc1c 4134  1 cpw1 4135   Nn cnnc 4373   cplc 4375   Fin cfin 4376  cop 4561  copab 4622   class class class wbr 4639  c1st 4717   S csset 4719   SI csi 4720   ccom 4721  cima 4722  ccnv 4771   crn 4773   cres 4774  cfv 4781  c2nd 4783  (class class class)co 5525   ctxp 5735  cfix 5739   AddC caddcfn 5745   Ins2 cins2 5749   Ins3 cins3 5751  Imagecimage 5753   Clos1 cclos1 5872   We cwe 5895   NC cncs 6088   c clec 6089   Nc cnc 6091   Tc ctc 6093  2cc2c 6094   ↑c cce 6096  TcFnctcfn 6097   Spac cspac 6273

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-13 1712  ax-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-xp 4079  ax-cnv 4080  ax-1c 4081  ax-sset 4082  ax-si 4083  ax-ins2 4084  ax-ins3 4085  ax-typlower 4086  ax-sn 4087

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-ral 2619  df-rex 2620  df-reu 2621  df-rmo 2622  df-rab 2623  df-v 2861  df-sbc 3047  df-csb 3137  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-symdif 3216  df-ss 3259  df-pss 3261  df-nul 3551  df-if 3663  df-pw 3724  df-sn 3741  df-pr 3742  df-uni 3892  df-int 3927  df-iun 3971  df-opk 4058  df-1c 4136  df-pw1 4137  df-uni1 4138  df-xpk 4185  df-cnvk 4186  df-ins2k 4187  df-ins3k 4188  df-imak 4189  df-cok 4190  df-p6 4191  df-sik 4192  df-ssetk 4193  df-imagek 4194  df-idk 4195  df-iota 4339  df-0c 4377  df-addc 4378  df-nnc 4379  df-fin 4380  df-lefin 4440  df-ltfin 4441  df-ncfin 4442  df-tfin 4443  df-evenfin 4444  df-oddfin 4445  df-sfin 4446  df-spfin 4447  df-phi 4565  df-op 4566  df-proj1 4567  df-proj2 4568  df-opab 4623  df-br 4640  df-1st 4723  df-swap 4724  df-sset 4725  df-co 4726  df-ima 4727  df-si 4728  df-id 4767  df-xp 4784  df-cnv 4785  df-rn 4786  df-dm 4787  df-res 4788  df-fun 4789  df-fn 4790  df-f 4791  df-f1 4792  df-fo 4793  df-f1o 4794  df-fv 4795  df-2nd 4797  df-ov 5526  df-oprab 5528  df-mpt 5652  df-mpt2 5654  df-txp 5736  df-fix 5740  df-cup 5742  df-disj 5744  df-addcfn 5746  df-ins2 5750  df-ins3 5752  df-image 5754  df-ins4 5756  df-si3 5758  df-funs 5760  df-fns 5762  df-pw1fn 5766  df-fullfun 5768  df-clos1 5873  df-trans 5899  df-sym 5908  df-er 5909  df-ec 5947  df-qs 5951  df-map 6001  df-en 6029  df-ncs 6098  df-nc 6101  df-tc 6103  df-2c 6104  df-ce 6106  df-tcfn 6107  df-spac 6274

This theorem is referenced by:  nchoicelem17  6305

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