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Mirrors > Home > ILE Home > Th. List > ov6g | Unicode version |
Description: The value of an operation class abstraction. Special case. (Contributed by NM, 13-Nov-2006.) |
Ref | Expression |
---|---|
ov6g.1 | |
ov6g.2 |
Ref | Expression |
---|---|
ov6g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ov 5745 | . 2 | |
2 | eqid 2117 | . . . . . 6 | |
3 | biidd 171 | . . . . . . 7 | |
4 | 3 | copsex2g 4138 | . . . . . 6 |
5 | 2, 4 | mpbiri 167 | . . . . 5 |
6 | 5 | 3adant3 986 | . . . 4 |
7 | 6 | adantr 274 | . . 3 |
8 | eqeq1 2124 | . . . . . . . 8 | |
9 | 8 | anbi1d 460 | . . . . . . 7 |
10 | ov6g.1 | . . . . . . . . . 10 | |
11 | 10 | eqeq2d 2129 | . . . . . . . . 9 |
12 | 11 | eqcoms 2120 | . . . . . . . 8 |
13 | 12 | pm5.32i 449 | . . . . . . 7 |
14 | 9, 13 | syl6bb 195 | . . . . . 6 |
15 | 14 | 2exbidv 1824 | . . . . 5 |
16 | eqeq1 2124 | . . . . . . 7 | |
17 | 16 | anbi2d 459 | . . . . . 6 |
18 | 17 | 2exbidv 1824 | . . . . 5 |
19 | moeq 2832 | . . . . . . 7 | |
20 | 19 | mosubop 4575 | . . . . . 6 |
21 | 20 | a1i 9 | . . . . 5 |
22 | ov6g.2 | . . . . . 6 | |
23 | dfoprab2 5786 | . . . . . 6 | |
24 | eleq1 2180 | . . . . . . . . . . . 12 | |
25 | 24 | anbi1d 460 | . . . . . . . . . . 11 |
26 | 25 | pm5.32i 449 | . . . . . . . . . 10 |
27 | an12 535 | . . . . . . . . . 10 | |
28 | 26, 27 | bitr3i 185 | . . . . . . . . 9 |
29 | 28 | 2exbii 1570 | . . . . . . . 8 |
30 | 19.42vv 1865 | . . . . . . . 8 | |
31 | 29, 30 | bitri 183 | . . . . . . 7 |
32 | 31 | opabbii 3965 | . . . . . 6 |
33 | 22, 23, 32 | 3eqtri 2142 | . . . . 5 |
34 | 15, 18, 21, 33 | fvopab3ig 5463 | . . . 4 |
35 | 34 | 3ad2antl3 1130 | . . 3 |
36 | 7, 35 | mpd 13 | . 2 |
37 | 1, 36 | syl5eq 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 947 wceq 1316 wex 1453 wcel 1465 wmo 1978 cop 3500 copab 3958 cfv 5093 (class class class)co 5742 coprab 5743 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-iota 5058 df-fun 5095 df-fv 5101 df-ov 5745 df-oprab 5746 |
This theorem is referenced by: (None) |
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