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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 5777 | . 2 | |
2 | eqid 2139 | . . . . . 6 | |
3 | biidd 171 | . . . . . . 7 | |
4 | 3 | copsex2g 4168 | . . . . . 6 |
5 | 2, 4 | mpbiri 167 | . . . . 5 |
6 | 5 | 3adant3 1001 | . . . 4 |
7 | 6 | adantr 274 | . . 3 |
8 | eqeq1 2146 | . . . . . . . 8 | |
9 | 8 | anbi1d 460 | . . . . . . 7 |
10 | ov6g.1 | . . . . . . . . . 10 | |
11 | 10 | eqeq2d 2151 | . . . . . . . . 9 |
12 | 11 | eqcoms 2142 | . . . . . . . 8 |
13 | 12 | pm5.32i 449 | . . . . . . 7 |
14 | 9, 13 | syl6bb 195 | . . . . . 6 |
15 | 14 | 2exbidv 1840 | . . . . 5 |
16 | eqeq1 2146 | . . . . . . 7 | |
17 | 16 | anbi2d 459 | . . . . . 6 |
18 | 17 | 2exbidv 1840 | . . . . 5 |
19 | moeq 2859 | . . . . . . 7 | |
20 | 19 | mosubop 4605 | . . . . . 6 |
21 | 20 | a1i 9 | . . . . 5 |
22 | ov6g.2 | . . . . . 6 | |
23 | dfoprab2 5818 | . . . . . 6 | |
24 | eleq1 2202 | . . . . . . . . . . . 12 | |
25 | 24 | anbi1d 460 | . . . . . . . . . . 11 |
26 | 25 | pm5.32i 449 | . . . . . . . . . 10 |
27 | an12 550 | . . . . . . . . . 10 | |
28 | 26, 27 | bitr3i 185 | . . . . . . . . 9 |
29 | 28 | 2exbii 1585 | . . . . . . . 8 |
30 | 19.42vv 1883 | . . . . . . . 8 | |
31 | 29, 30 | bitri 183 | . . . . . . 7 |
32 | 31 | opabbii 3995 | . . . . . 6 |
33 | 22, 23, 32 | 3eqtri 2164 | . . . . 5 |
34 | 15, 18, 21, 33 | fvopab3ig 5495 | . . . 4 |
35 | 34 | 3ad2antl3 1145 | . . 3 |
36 | 7, 35 | mpd 13 | . 2 |
37 | 1, 36 | syl5eq 2184 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wceq 1331 wex 1468 wcel 1480 wmo 2000 cop 3530 copab 3988 cfv 5123 (class class class)co 5774 coprab 5775 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-iota 5088 df-fun 5125 df-fv 5131 df-ov 5777 df-oprab 5778 |
This theorem is referenced by: (None) |
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