Step | Hyp | Ref
| Expression |
1 | | 1stfcl.t |
. . . 4
c |
2 | | eqid 2622 |
. . . . 5
|
3 | | eqid 2622 |
. . . . 5
|
4 | 1, 2, 3 | xpcbas 16818 |
. . . 4
|
5 | | eqid 2622 |
. . . 4
|
6 | | 1stfcl.c |
. . . 4
|
7 | | 1stfcl.d |
. . . 4
|
8 | | 1stfcl.p |
. . . 4
F
|
9 | 1, 4, 5, 6, 7, 8 | 1stfval 16831 |
. . 3
|
10 | | fo1st 7188 |
. . . . . . . 8
|
11 | | fofun 6116 |
. . . . . . . 8
|
12 | 10, 11 | ax-mp 5 |
. . . . . . 7
|
13 | | fvex 6201 |
. . . . . . . 8
|
14 | | fvex 6201 |
. . . . . . . 8
|
15 | 13, 14 | xpex 6962 |
. . . . . . 7
|
16 | | resfunexg 6479 |
. . . . . . 7
|
17 | 12, 15, 16 | mp2an 708 |
. . . . . 6
|
18 | 15, 15 | mpt2ex 7247 |
. . . . . 6
|
19 | 17, 18 | op2ndd 7179 |
. . . . 5
|
20 | 9, 19 | syl 17 |
. . . 4
|
21 | 20 | opeq2d 4409 |
. . 3
|
22 | 9, 21 | eqtr4d 2659 |
. 2
|
23 | | eqid 2622 |
. . . 4
|
24 | | eqid 2622 |
. . . 4
|
25 | | eqid 2622 |
. . . 4
|
26 | | eqid 2622 |
. . . 4
comp comp |
27 | | eqid 2622 |
. . . 4
comp comp |
28 | 1, 6, 7 | xpccat 16830 |
. . . 4
|
29 | | f1stres 7190 |
. . . . 5
|
30 | 29 | a1i 11 |
. . . 4
|
31 | | eqid 2622 |
. . . . . 6
|
32 | | ovex 6678 |
. . . . . . 7
|
33 | | resfunexg 6479 |
. . . . . . 7
|
34 | 12, 32, 33 | mp2an 708 |
. . . . . 6
|
35 | 31, 34 | fnmpt2i 7239 |
. . . . 5
|
36 | 20 | fneq1d 5981 |
. . . . 5
|
37 | 35, 36 | mpbiri 248 |
. . . 4
|
38 | | f1stres 7190 |
. . . . . 6
|
39 | 6 | adantr 481 |
. . . . . . . . 9
|
40 | 7 | adantr 481 |
. . . . . . . . 9
|
41 | | simprl 794 |
. . . . . . . . 9
|
42 | | simprr 796 |
. . . . . . . . 9
|
43 | 1, 4, 5, 39, 40, 8, 41, 42 | 1stf2 16833 |
. . . . . . . 8
|
44 | | eqid 2622 |
. . . . . . . . . 10
|
45 | 1, 4, 23, 44, 5, 41, 42 | xpchom 16820 |
. . . . . . . . 9
|
46 | 45 | reseq2d 5396 |
. . . . . . . 8
|
47 | 43, 46 | eqtrd 2656 |
. . . . . . 7
|
48 | 47 | feq1d 6030 |
. . . . . 6
|
49 | 38, 48 | mpbiri 248 |
. . . . 5
|
50 | | fvres 6207 |
. . . . . . . 8
|
51 | 50 | ad2antrl 764 |
. . . . . . 7
|
52 | | fvres 6207 |
. . . . . . . 8
|
53 | 52 | ad2antll 765 |
. . . . . . 7
|
54 | 51, 53 | oveq12d 6668 |
. . . . . 6
|
55 | 45, 54 | feq23d 6040 |
. . . . 5
|
56 | 49, 55 | mpbird 247 |
. . . 4
|
57 | 28 | adantr 481 |
. . . . . . . 8
|
58 | | simpr 477 |
. . . . . . . 8
|
59 | 4, 5, 24, 57, 58 | catidcl 16343 |
. . . . . . 7
|
60 | | fvres 6207 |
. . . . . . 7
|
61 | 59, 60 | syl 17 |
. . . . . 6
|
62 | | 1st2nd2 7205 |
. . . . . . . . . 10
|
63 | 62 | adantl 482 |
. . . . . . . . 9
|
64 | 63 | fveq2d 6195 |
. . . . . . . 8
|
65 | 6 | adantr 481 |
. . . . . . . . 9
|
66 | 7 | adantr 481 |
. . . . . . . . 9
|
67 | | eqid 2622 |
. . . . . . . . 9
|
68 | | xp1st 7198 |
. . . . . . . . . 10
|
69 | 68 | adantl 482 |
. . . . . . . . 9
|
70 | | xp2nd 7199 |
. . . . . . . . . 10
|
71 | 70 | adantl 482 |
. . . . . . . . 9
|
72 | 1, 65, 66, 2, 3, 25, 67, 24, 69, 71 | xpcid 16829 |
. . . . . . . 8
|
73 | 64, 72 | eqtrd 2656 |
. . . . . . 7
|
74 | | fvex 6201 |
. . . . . . . 8
|
75 | | fvex 6201 |
. . . . . . . 8
|
76 | 74, 75 | op1std 7178 |
. . . . . . 7
|
77 | 73, 76 | syl 17 |
. . . . . 6
|
78 | 61, 77 | eqtrd 2656 |
. . . . 5
|
79 | 1, 4, 5, 65, 66, 8, 58, 58 | 1stf2 16833 |
. . . . . 6
|
80 | 79 | fveq1d 6193 |
. . . . 5
|
81 | 50 | adantl 482 |
. . . . . 6
|
82 | 81 | fveq2d 6195 |
. . . . 5
|
83 | 78, 80, 82 | 3eqtr4d 2666 |
. . . 4
|
84 | 28 | 3ad2ant1 1082 |
. . . . . . . 8
|
85 | | simp21 1094 |
. . . . . . . 8
|
86 | | simp22 1095 |
. . . . . . . 8
|
87 | | simp23 1096 |
. . . . . . . 8
|
88 | | simp3l 1089 |
. . . . . . . 8
|
89 | | simp3r 1090 |
. . . . . . . 8
|
90 | 4, 5, 26, 84, 85, 86, 87, 88, 89 | catcocl 16346 |
. . . . . . 7
comp |
91 | | fvres 6207 |
. . . . . . 7
comp comp comp |
92 | 90, 91 | syl 17 |
. . . . . 6
comp comp |
93 | 1, 4, 5, 26, 85, 86, 87, 88, 89, 27 | xpcco1st 16824 |
. . . . . 6
comp comp |
94 | 92, 93 | eqtrd 2656 |
. . . . 5
comp comp |
95 | 6 | 3ad2ant1 1082 |
. . . . . . 7
|
96 | 7 | 3ad2ant1 1082 |
. . . . . . 7
|
97 | 1, 4, 5, 95, 96, 8, 85, 87 | 1stf2 16833 |
. . . . . 6
|
98 | 97 | fveq1d 6193 |
. . . . 5
comp
comp |
99 | 85, 50 | syl 17 |
. . . . . . . 8
|
100 | 86, 52 | syl 17 |
. . . . . . . 8
|
101 | 99, 100 | opeq12d 4410 |
. . . . . . 7
|
102 | | fvres 6207 |
. . . . . . . 8
|
103 | 87, 102 | syl 17 |
. . . . . . 7
|
104 | 101, 103 | oveq12d 6668 |
. . . . . 6
comp
comp |
105 | 1, 4, 5, 95, 96, 8, 86, 87 | 1stf2 16833 |
. . . . . . . 8
|
106 | 105 | fveq1d 6193 |
. . . . . . 7
|
107 | | fvres 6207 |
. . . . . . . 8
|
108 | 89, 107 | syl 17 |
. . . . . . 7
|
109 | 106, 108 | eqtrd 2656 |
. . . . . 6
|
110 | 1, 4, 5, 95, 96, 8, 85, 86 | 1stf2 16833 |
. . . . . . . 8
|
111 | 110 | fveq1d 6193 |
. . . . . . 7
|
112 | | fvres 6207 |
. . . . . . . 8
|
113 | 88, 112 | syl 17 |
. . . . . . 7
|
114 | 111, 113 | eqtrd 2656 |
. . . . . 6
|
115 | 104, 109,
114 | oveq123d 6671 |
. . . . 5
comp
comp |
116 | 94, 98, 115 | 3eqtr4d 2666 |
. . . 4
comp comp
|
117 | 4, 2, 5, 23, 24, 25, 26, 27, 28, 6, 30, 37, 56, 83, 116 | isfuncd 16525 |
. . 3
|
118 | | df-br 4654 |
. . 3
|
119 | 117, 118 | sylib 208 |
. 2
|
120 | 22, 119 | eqeltrd 2701 |
1
|