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Mirrors > Home > ILE Home > Th. List > copsex4g | Unicode version |
Description: An implicit substitution inference for 2 ordered pairs. (Contributed by NM, 5-Aug-1995.) |
Ref | Expression |
---|---|
copsex4g.1 |
Ref | Expression |
---|---|
copsex4g |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqcom 2166 | . . . . . . 7 | |
2 | vex 2724 | . . . . . . . 8 | |
3 | vex 2724 | . . . . . . . 8 | |
4 | 2, 3 | opth 4209 | . . . . . . 7 |
5 | 1, 4 | bitri 183 | . . . . . 6 |
6 | eqcom 2166 | . . . . . . 7 | |
7 | vex 2724 | . . . . . . . 8 | |
8 | vex 2724 | . . . . . . . 8 | |
9 | 7, 8 | opth 4209 | . . . . . . 7 |
10 | 6, 9 | bitri 183 | . . . . . 6 |
11 | 5, 10 | anbi12i 456 | . . . . 5 |
12 | 11 | anbi1i 454 | . . . 4 |
13 | 12 | a1i 9 | . . 3 |
14 | 13 | 4exbidv 1857 | . 2 |
15 | id 19 | . . 3 | |
16 | copsex4g.1 | . . 3 | |
17 | 15, 16 | cgsex4g 2758 | . 2 |
18 | 14, 17 | bitrd 187 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 cop 3573 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 |
This theorem is referenced by: opbrop 4677 ovi3 5969 dfplpq2 7286 dfmpq2 7287 enq0breq 7368 |
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