Theorem fmtno5lem4 41468

Description: Lemma 4 for fmtno5 41469. (Contributed by AV, 30-Jul-2021.)

Assertion

Ref	Expression
fmtno5lem4	|- (;;;; 6 5 5 3 6 ^ 2 ) = ;;;;;;;;; 4 2 9 4 9 6 7 2 9 6

Proof of Theorem fmtno5lem4

Step	Hyp	Ref	Expression
1		6nn0 11313	. . . . . . . 8 |- 6 e. NN0
2		5nn0 11312	. . . . . . . 8 |- 5 e. NN0
3	1, 2	deccl 11512	. . . . . . 7 |- ; 6 5 e. NN0
4	3, 2	deccl 11512	. . . . . 6 |- ;; 6 5 5 e. NN0
5		3nn0 11310	. . . . . 6 |- 3 e. NN0
6	4, 5	deccl 11512	. . . . 5 |- ;;; 6 5 5 3 e. NN0
7	6, 1	deccl 11512	. . . 4 |- ;;;; 6 5 5 3 6 e. NN0
8	7	nn0cni 11304	. . 3 |- ;;;; 6 5 5 3 6 e. CC
9	8	sqvali 12943	. 2 |- (;;;; 6 5 5 3 6 ^ 2 ) = (;;;; 6 5 5 3 6 x. ;;;; 6 5 5 3 6 )
10		fmtno5lem1 41465	. . . . . . . . . 10 |- (;;;; 6 5 5 3 6 x. 6 ) = ;;;;; 3 9 3 2 1 6
11	10	eqcomi 2631	. . . . . . . . 9 |- ;;;;; 3 9 3 2 1 6 = (;;;; 6 5 5 3 6 x. 6 )
12		fmtno5lem2 41466	. . . . . . . . . 10 |- (;;;; 6 5 5 3 6 x. 5 ) = ;;;;; 3 2 7 6 8 0
13	12	eqcomi 2631	. . . . . . . . 9 |- ;;;;; 3 2 7 6 8 0 = (;;;; 6 5 5 3 6 x. 5 )
14	1, 2, 7, 11, 13	decmul10add 11593	. . . . . . . 8 |- (;;;; 6 5 5 3 6 x. ; 6 5 ) = (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 )
15	14	eqcomi 2631	. . . . . . 7 |- (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) = (;;;; 6 5 5 3 6 x. ; 6 5 )
16	3, 2, 7, 15, 13	decmul10add 11593	. . . . . 6 |- (;;;; 6 5 5 3 6 x. ;; 6 5 5 ) = (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 )
17	16	eqcomi 2631	. . . . 5 |- (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) = (;;;; 6 5 5 3 6 x. ;; 6 5 5 )
18		fmtno5lem3 41467	. . . . . 6 |- (;;;; 6 5 5 3 6 x. 3 ) = ;;;;; 1 9 6 6 0 8
19	18	eqcomi 2631	. . . . 5 |- ;;;;; 1 9 6 6 0 8 = (;;;; 6 5 5 3 6 x. 3 )
20	4, 5, 7, 17, 19	decmul10add 11593	. . . 4 |- (;;;; 6 5 5 3 6 x. ;;; 6 5 5 3 ) = (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 )
21	20	eqcomi 2631	. . 3 |- (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 ) = (;;;; 6 5 5 3 6 x. ;;; 6 5 5 3 )
22	6, 1, 7, 21, 11	decmul10add 11593	. 2 |- (;;;; 6 5 5 3 6 x. ;;;; 6 5 5 3 6 ) = (; (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 ) 0 + ;;;;; 3 9 3 2 1 6 )
23		4nn0 11311	. . . . . . . . . . 11 |- 4 e. NN0
24		2nn0 11309	. . . . . . . . . . 11 |- 2 e. NN0
25	23, 24	deccl 11512	. . . . . . . . . 10 |- ; 4 2 e. NN0
26		9nn0 11316	. . . . . . . . . 10 |- 9 e. NN0
27	25, 26	deccl 11512	. . . . . . . . 9 |- ;; 4 2 9 e. NN0
28	27, 23	deccl 11512	. . . . . . . 8 |- ;;; 4 2 9 4 e. NN0
29	28, 2	deccl 11512	. . . . . . 7 |- ;;;; 4 2 9 4 5 e. NN0
30		7nn0 11314	. . . . . . 7 |- 7 e. NN0
31	29, 30	deccl 11512	. . . . . 6 |- ;;;;; 4 2 9 4 5 7 e. NN0
32	31, 23	deccl 11512	. . . . 5 |- ;;;;;; 4 2 9 4 5 7 4 e. NN0
33		0nn0 11307	. . . . 5 |- 0 e. NN0
34	32, 33	deccl 11512	. . . 4 |- ;;;;;;; 4 2 9 4 5 7 4 0 e. NN0
35		8nn0 11315	. . . 4 |- 8 e. NN0
36	34, 35	deccl 11512	. . 3 |- ;;;;;;;; 4 2 9 4 5 7 4 0 8 e. NN0
37	5, 26	deccl 11512	. . . . . 6 |- ; 3 9 e. NN0
38	37, 5	deccl 11512	. . . . 5 |- ;; 3 9 3 e. NN0
39	38, 24	deccl 11512	. . . 4 |- ;;; 3 9 3 2 e. NN0
40		1nn0 11308	. . . 4 |- 1 e. NN0
41	39, 40	deccl 11512	. . 3 |- ;;;; 3 9 3 2 1 e. NN0
42	27, 24	deccl 11512	. . . . . . . . 9 |- ;;; 4 2 9 2 e. NN0
43	42, 1	deccl 11512	. . . . . . . 8 |- ;;;; 4 2 9 2 6 e. NN0
44	43, 33	deccl 11512	. . . . . . 7 |- ;;;;; 4 2 9 2 6 0 e. NN0
45	44, 35	deccl 11512	. . . . . 6 |- ;;;;;; 4 2 9 2 6 0 8 e. NN0
46	45, 33	deccl 11512	. . . . 5 |- ;;;;;;; 4 2 9 2 6 0 8 0 e. NN0
47	40, 26	deccl 11512	. . . . . . . 8 |- ; 1 9 e. NN0
48	47, 1	deccl 11512	. . . . . . 7 |- ;; 1 9 6 e. NN0
49	48, 1	deccl 11512	. . . . . 6 |- ;;; 1 9 6 6 e. NN0
50	49, 33	deccl 11512	. . . . 5 |- ;;;; 1 9 6 6 0 e. NN0
51	25, 2	deccl 11512	. . . . . . . . . . 11 |- ;; 4 2 5 e. NN0
52	51, 26	deccl 11512	. . . . . . . . . 10 |- ;;; 4 2 5 9 e. NN0
53	52, 35	deccl 11512	. . . . . . . . 9 |- ;;;; 4 2 5 9 8 e. NN0
54	53, 23	deccl 11512	. . . . . . . 8 |- ;;;;; 4 2 5 9 8 4 e. NN0
55	54, 33	deccl 11512	. . . . . . 7 |- ;;;;;; 4 2 5 9 8 4 0 e. NN0
56	5, 24	deccl 11512	. . . . . . . . . 10 |- ; 3 2 e. NN0
57	56, 30	deccl 11512	. . . . . . . . 9 |- ;; 3 2 7 e. NN0
58	57, 1	deccl 11512	. . . . . . . 8 |- ;;; 3 2 7 6 e. NN0
59	58, 35	deccl 11512	. . . . . . 7 |- ;;;; 3 2 7 6 8 e. NN0
60	41, 1	deccl 11512	. . . . . . . . 9 |- ;;;;; 3 9 3 2 1 6 e. NN0
61		eqid 2622	. . . . . . . . 9 |- ;;;;;; 3 9 3 2 1 6 0 = ;;;;;; 3 9 3 2 1 6 0
62		eqid 2622	. . . . . . . . 9 |- ;;;;; 3 2 7 6 8 0 = ;;;;; 3 2 7 6 8 0
63		eqid 2622	. . . . . . . . . 10 |- ;;;;; 3 9 3 2 1 6 = ;;;;; 3 9 3 2 1 6
64		eqid 2622	. . . . . . . . . 10 |- ;;;; 3 2 7 6 8 = ;;;; 3 2 7 6 8
65		7p1e8 11157	. . . . . . . . . . 11 |- ( 7 + 1 ) = 8
66		eqid 2622	. . . . . . . . . . . 12 |- ;;;; 3 9 3 2 1 = ;;;; 3 9 3 2 1
67		eqid 2622	. . . . . . . . . . . 12 |- ;;; 3 2 7 6 = ;;; 3 2 7 6
68		eqid 2622	. . . . . . . . . . . . 13 |- ;;; 3 9 3 2 = ;;; 3 9 3 2
69		eqid 2622	. . . . . . . . . . . . 13 |- ;; 3 2 7 = ;; 3 2 7
70		eqid 2622	. . . . . . . . . . . . . 14 |- ;; 3 9 3 = ;; 3 9 3
71		eqid 2622	. . . . . . . . . . . . . 14 |- ; 3 2 = ; 3 2
72		eqid 2622	. . . . . . . . . . . . . . 15 |- ; 3 9 = ; 3 9
73		3p1e4 11153	. . . . . . . . . . . . . . 15 |- ( 3 + 1 ) = 4
74		9p3e12 11621	. . . . . . . . . . . . . . 15 |- ( 9 + 3 ) = ; 1 2
75	5, 26, 5, 72, 73, 24, 74	decaddci 11580	. . . . . . . . . . . . . 14 |- (; 3 9 + 3 ) = ; 4 2
76		3p2e5 11160	. . . . . . . . . . . . . 14 |- ( 3 + 2 ) = 5
77	37, 5, 5, 24, 70, 71, 75, 76	decadd 11570	. . . . . . . . . . . . 13 |- (;; 3 9 3 + ; 3 2 ) = ;; 4 2 5
78		7cn 11104	. . . . . . . . . . . . . 14 |- 7 e. CC
79		2cn 11091	. . . . . . . . . . . . . 14 |- 2 e. CC
80		7p2e9 11172	. . . . . . . . . . . . . 14 |- ( 7 + 2 ) = 9
81	78, 79, 80	addcomli 10228	. . . . . . . . . . . . 13 |- ( 2 + 7 ) = 9
82	38, 24, 56, 30, 68, 69, 77, 81	decadd 11570	. . . . . . . . . . . 12 |- (;;; 3 9 3 2 + ;; 3 2 7 ) = ;;; 4 2 5 9
83		6cn 11102	. . . . . . . . . . . . 13 |- 6 e. CC
84		ax-1cn 9994	. . . . . . . . . . . . 13 |- 1 e. CC
85		6p1e7 11156	. . . . . . . . . . . . 13 |- ( 6 + 1 ) = 7
86	83, 84, 85	addcomli 10228	. . . . . . . . . . . 12 |- ( 1 + 6 ) = 7
87	39, 40, 57, 1, 66, 67, 82, 86	decadd 11570	. . . . . . . . . . 11 |- (;;;; 3 9 3 2 1 + ;;; 3 2 7 6 ) = ;;;; 4 2 5 9 7
88	52, 30, 65, 87	decsuc 11535	. . . . . . . . . 10 |- ( (;;;; 3 9 3 2 1 + ;;; 3 2 7 6 ) + 1 ) = ;;;; 4 2 5 9 8
89		8cn 11106	. . . . . . . . . . 11 |- 8 e. CC
90		8p6e14 11616	. . . . . . . . . . 11 |- ( 8 + 6 ) = ; 1 4
91	89, 83, 90	addcomli 10228	. . . . . . . . . 10 |- ( 6 + 8 ) = ; 1 4
92	41, 1, 58, 35, 63, 64, 88, 23, 91	decaddc 11572	. . . . . . . . 9 |- (;;;;; 3 9 3 2 1 6 + ;;;; 3 2 7 6 8 ) = ;;;;; 4 2 5 9 8 4
93		00id 10211	. . . . . . . . 9 |- ( 0 + 0 ) = 0
94	60, 33, 59, 33, 61, 62, 92, 93	decadd 11570	. . . . . . . 8 |- (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) = ;;;;;; 4 2 5 9 8 4 0
95	94	deceq1i 11504	. . . . . . 7 |- ; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 = ;;;;;;; 4 2 5 9 8 4 0 0
96		eqid 2622	. . . . . . . 8 |- ;;;;;; 4 2 5 9 8 4 0 = ;;;;;; 4 2 5 9 8 4 0
97		eqid 2622	. . . . . . . . 9 |- ;;;;; 4 2 5 9 8 4 = ;;;;; 4 2 5 9 8 4
98		5p1e6 11155	. . . . . . . . . 10 |- ( 5 + 1 ) = 6
99		eqid 2622	. . . . . . . . . . 11 |- ;;;; 4 2 5 9 8 = ;;;; 4 2 5 9 8
100		1p1e2 11134	. . . . . . . . . . . 12 |- ( 1 + 1 ) = 2
101		eqid 2622	. . . . . . . . . . . . 13 |- ;;; 4 2 5 9 = ;;; 4 2 5 9
102		8p1e9 11158	. . . . . . . . . . . . . 14 |- ( 8 + 1 ) = 9
103		eqid 2622	. . . . . . . . . . . . . . 15 |- ;; 4 2 5 = ;; 4 2 5
104		5p3e8 11166	. . . . . . . . . . . . . . 15 |- ( 5 + 3 ) = 8
105	25, 2, 5, 103, 104	decaddi 11579	. . . . . . . . . . . . . 14 |- (;; 4 2 5 + 3 ) = ;; 4 2 8
106	25, 35, 102, 105	decsuc 11535	. . . . . . . . . . . . 13 |- ( (;; 4 2 5 + 3 ) + 1 ) = ;; 4 2 9
107		9p2e11 11619	. . . . . . . . . . . . 13 |- ( 9 + 2 ) = ; 1 1
108	51, 26, 5, 24, 101, 71, 106, 40, 107	decaddc 11572	. . . . . . . . . . . 12 |- (;;; 4 2 5 9 + ; 3 2 ) = ;;; 4 2 9 1
109	27, 40, 100, 108	decsuc 11535	. . . . . . . . . . 11 |- ( (;;; 4 2 5 9 + ; 3 2 ) + 1 ) = ;;; 4 2 9 2
110		8p7e15 11617	. . . . . . . . . . 11 |- ( 8 + 7 ) = ; 1 5
111	52, 35, 56, 30, 99, 69, 109, 2, 110	decaddc 11572	. . . . . . . . . 10 |- (;;;; 4 2 5 9 8 + ;; 3 2 7 ) = ;;;; 4 2 9 2 5
112	42, 2, 98, 111	decsuc 11535	. . . . . . . . 9 |- ( (;;;; 4 2 5 9 8 + ;; 3 2 7 ) + 1 ) = ;;;; 4 2 9 2 6
113		4cn 11098	. . . . . . . . . 10 |- 4 e. CC
114		6p4e10 11598	. . . . . . . . . 10 |- ( 6 + 4 ) = ; 1 0
115	83, 113, 114	addcomli 10228	. . . . . . . . 9 |- ( 4 + 6 ) = ; 1 0
116	53, 23, 57, 1, 97, 67, 112, 33, 115	decaddc 11572	. . . . . . . 8 |- (;;;;; 4 2 5 9 8 4 + ;;; 3 2 7 6 ) = ;;;;; 4 2 9 2 6 0
117	89	addid2i 10224	. . . . . . . 8 |- ( 0 + 8 ) = 8
118	54, 33, 58, 35, 96, 64, 116, 117	decadd 11570	. . . . . . 7 |- (;;;;;; 4 2 5 9 8 4 0 + ;;;; 3 2 7 6 8 ) = ;;;;;; 4 2 9 2 6 0 8
119	55, 33, 59, 33, 95, 62, 118, 93	decadd 11570	. . . . . 6 |- (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) = ;;;;;;; 4 2 9 2 6 0 8 0
120	119	deceq1i 11504	. . . . 5 |- ; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 = ;;;;;;;; 4 2 9 2 6 0 8 0 0
121		eqid 2622	. . . . 5 |- ;;;;; 1 9 6 6 0 8 = ;;;;; 1 9 6 6 0 8
122	45, 49	decaddm10 11578	. . . . . 6 |- (;;;;;;; 4 2 9 2 6 0 8 0 + ;;;; 1 9 6 6 0 ) = ; (;;;;;; 4 2 9 2 6 0 8 + ;;; 1 9 6 6 ) 0
123		eqid 2622	. . . . . . . 8 |- ;;;;;; 4 2 9 2 6 0 8 = ;;;;;; 4 2 9 2 6 0 8
124		eqid 2622	. . . . . . . 8 |- ;;; 1 9 6 6 = ;;; 1 9 6 6
125		eqid 2622	. . . . . . . . . 10 |- ;;;;; 4 2 9 2 6 0 = ;;;;; 4 2 9 2 6 0
126		eqid 2622	. . . . . . . . . 10 |- ;; 1 9 6 = ;; 1 9 6
127		eqid 2622	. . . . . . . . . . 11 |- ;;;; 4 2 9 2 6 = ;;;; 4 2 9 2 6
128		eqid 2622	. . . . . . . . . . 11 |- ; 1 9 = ; 1 9
129		2p1e3 11151	. . . . . . . . . . . . 13 |- ( 2 + 1 ) = 3
130		eqid 2622	. . . . . . . . . . . . 13 |- ;;; 4 2 9 2 = ;;; 4 2 9 2
131	27, 24, 129, 130	decsuc 11535	. . . . . . . . . . . 12 |- (;;; 4 2 9 2 + 1 ) = ;;; 4 2 9 3
132	27, 5, 73, 131	decsuc 11535	. . . . . . . . . . 11 |- ( (;;; 4 2 9 2 + 1 ) + 1 ) = ;;; 4 2 9 4
133		9cn 11108	. . . . . . . . . . . 12 |- 9 e. CC
134		9p6e15 11624	. . . . . . . . . . . 12 |- ( 9 + 6 ) = ; 1 5
135	133, 83, 134	addcomli 10228	. . . . . . . . . . 11 |- ( 6 + 9 ) = ; 1 5
136	42, 1, 40, 26, 127, 128, 132, 2, 135	decaddc 11572	. . . . . . . . . 10 |- (;;;; 4 2 9 2 6 + ; 1 9 ) = ;;;; 4 2 9 4 5
137	83	addid2i 10224	. . . . . . . . . 10 |- ( 0 + 6 ) = 6
138	43, 33, 47, 1, 125, 126, 136, 137	decadd 11570	. . . . . . . . 9 |- (;;;;; 4 2 9 2 6 0 + ;; 1 9 6 ) = ;;;;; 4 2 9 4 5 6
139	29, 1, 85, 138	decsuc 11535	. . . . . . . 8 |- ( (;;;;; 4 2 9 2 6 0 + ;; 1 9 6 ) + 1 ) = ;;;;; 4 2 9 4 5 7
140	44, 35, 48, 1, 123, 124, 139, 23, 90	decaddc 11572	. . . . . . 7 |- (;;;;;; 4 2 9 2 6 0 8 + ;;; 1 9 6 6 ) = ;;;;;; 4 2 9 4 5 7 4
141	140	deceq1i 11504	. . . . . 6 |- ; (;;;;;; 4 2 9 2 6 0 8 + ;;; 1 9 6 6 ) 0 = ;;;;;;; 4 2 9 4 5 7 4 0
142	122, 141	eqtri 2644	. . . . 5 |- (;;;;;;; 4 2 9 2 6 0 8 0 + ;;;; 1 9 6 6 0 ) = ;;;;;;; 4 2 9 4 5 7 4 0
143	46, 33, 50, 35, 120, 121, 142, 117	decadd 11570	. . . 4 |- (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 ) = ;;;;;;;; 4 2 9 4 5 7 4 0 8
144	143	deceq1i 11504	. . 3 |- ; (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 ) 0 = ;;;;;;;;; 4 2 9 4 5 7 4 0 8 0
145		eqid 2622	. . . 4 |- ;;;;;;;; 4 2 9 4 5 7 4 0 8 = ;;;;;;;; 4 2 9 4 5 7 4 0 8
146		eqid 2622	. . . . 5 |- ;;;;;;; 4 2 9 4 5 7 4 0 = ;;;;;;; 4 2 9 4 5 7 4 0
147		eqid 2622	. . . . . 6 |- ;;;;;; 4 2 9 4 5 7 4 = ;;;;;; 4 2 9 4 5 7 4
148		eqid 2622	. . . . . . 7 |- ;;;;; 4 2 9 4 5 7 = ;;;;; 4 2 9 4 5 7
149		eqid 2622	. . . . . . . . 9 |- ;;;; 4 2 9 4 5 = ;;;; 4 2 9 4 5
150	28, 2, 5, 149, 104	decaddi 11579	. . . . . . . 8 |- (;;;; 4 2 9 4 5 + 3 ) = ;;;; 4 2 9 4 8
151	28, 35, 102, 150	decsuc 11535	. . . . . . 7 |- ( (;;;; 4 2 9 4 5 + 3 ) + 1 ) = ;;;; 4 2 9 4 9
152		9p7e16 11625	. . . . . . . 8 |- ( 9 + 7 ) = ; 1 6
153	133, 78, 152	addcomli 10228	. . . . . . 7 |- ( 7 + 9 ) = ; 1 6
154	29, 30, 5, 26, 148, 72, 151, 1, 153	decaddc 11572	. . . . . 6 |- (;;;;; 4 2 9 4 5 7 + ; 3 9 ) = ;;;;; 4 2 9 4 9 6
155		4p3e7 11163	. . . . . 6 |- ( 4 + 3 ) = 7
156	31, 23, 37, 5, 147, 70, 154, 155	decadd 11570	. . . . 5 |- (;;;;;; 4 2 9 4 5 7 4 + ;; 3 9 3 ) = ;;;;;; 4 2 9 4 9 6 7
157	79	addid2i 10224	. . . . 5 |- ( 0 + 2 ) = 2
158	32, 33, 38, 24, 146, 68, 156, 157	decadd 11570	. . . 4 |- (;;;;;;; 4 2 9 4 5 7 4 0 + ;;; 3 9 3 2 ) = ;;;;;;; 4 2 9 4 9 6 7 2
159	34, 35, 39, 40, 145, 66, 158, 102	decadd 11570	. . 3 |- (;;;;;;;; 4 2 9 4 5 7 4 0 8 + ;;;; 3 9 3 2 1 ) = ;;;;;;;; 4 2 9 4 9 6 7 2 9
160	36, 33, 41, 1, 144, 63, 159, 137	decadd 11570	. 2 |- (; (; (; (;;;;;; 3 9 3 2 1 6 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 3 2 7 6 8 0 ) 0 + ;;;;; 1 9 6 6 0 8 ) 0 + ;;;;; 3 9 3 2 1 6 ) = ;;;;;;;;; 4 2 9 4 9 6 7 2 9 6
161	9, 22, 160	3eqtri 2648	1 |- (;;;; 6 5 5 3 6 ^ 2 ) = ;;;;;;;;; 4 2 9 4 9 6 7 2 9 6

Syntax hints:   = wceq 1483  (class class class)co 6650   0cc0 9936   1c1 9937   + caddc 9939   x. cmul 9941   2c2 11070   3c3 11071   4c4 11072   5c5 11073   6c6 11074   7c7 11075   8c8 11076   9c9 11077  ;cdc 11493   ^cexp 12860

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-8 1992  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602  ax-sep 4781  ax-nul 4789  ax-pow 4843  ax-pr 4906  ax-un 6949  ax-cnex 9992  ax-resscn 9993  ax-1cn 9994  ax-icn 9995  ax-addcl 9996  ax-addrcl 9997  ax-mulcl 9998  ax-mulrcl 9999  ax-mulcom 10000  ax-addass 10001  ax-mulass 10002  ax-distr 10003  ax-i2m1 10004  ax-1ne0 10005  ax-1rid 10006  ax-rnegex 10007  ax-rrecex 10008  ax-cnre 10009  ax-pre-lttri 10010  ax-pre-lttrn 10011  ax-pre-ltadd 10012  ax-pre-mulgt0 10013

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3or 1038  df-3an 1039  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-eu 2474  df-mo 2475  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-nel 2898  df-ral 2917  df-rex 2918  df-reu 2919  df-rab 2921  df-v 3202  df-sbc 3436  df-csb 3534  df-dif 3577  df-un 3579  df-in 3581  df-ss 3588  df-pss 3590  df-nul 3916  df-if 4087  df-pw 4160  df-sn 4178  df-pr 4180  df-tp 4182  df-op 4184  df-uni 4437  df-iun 4522  df-br 4654  df-opab 4713  df-mpt 4730  df-tr 4753  df-id 5024  df-eprel 5029  df-po 5035  df-so 5036  df-fr 5073  df-we 5075  df-xp 5120  df-rel 5121  df-cnv 5122  df-co 5123  df-dm 5124  df-rn 5125  df-res 5126  df-ima 5127  df-pred 5680  df-ord 5726  df-on 5727  df-lim 5728  df-suc 5729  df-iota 5851  df-fun 5890  df-fn 5891  df-f 5892  df-f1 5893  df-fo 5894  df-f1o 5895  df-fv 5896  df-riota 6611  df-ov 6653  df-oprab 6654  df-mpt2 6655  df-om 7066  df-2nd 7169  df-wrecs 7407  df-recs 7468  df-rdg 7506  df-er 7742  df-en 7956  df-dom 7957  df-sdom 7958  df-pnf 10076  df-mnf 10077  df-xr 10078  df-ltxr 10079  df-le 10080  df-sub 10268  df-neg 10269  df-nn 11021  df-2 11079  df-3 11080  df-4 11081  df-5 11082  df-6 11083  df-7 11084  df-8 11085  df-9 11086  df-n0 11293  df-z 11378  df-dec 11494  df-uz 11688  df-seq 12802  df-exp 12861

This theorem is referenced by:  fmtno5  41469