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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 2042 | . . . . . . 7 | |
2 | vex 2560 | . . . . . . . 8 | |
3 | vex 2560 | . . . . . . . 8 | |
4 | 2, 3 | opth 3974 | . . . . . . 7 |
5 | 1, 4 | bitri 173 | . . . . . 6 |
6 | eqcom 2042 | . . . . . . 7 | |
7 | vex 2560 | . . . . . . . 8 | |
8 | vex 2560 | . . . . . . . 8 | |
9 | 7, 8 | opth 3974 | . . . . . . 7 |
10 | 6, 9 | bitri 173 | . . . . . 6 |
11 | 5, 10 | anbi12i 433 | . . . . 5 |
12 | 11 | anbi1i 431 | . . . 4 |
13 | 12 | a1i 9 | . . 3 |
14 | 13 | 4exbidv 1750 | . 2 |
15 | id 19 | . . 3 | |
16 | copsex4g.1 | . . 3 | |
17 | 15, 16 | cgsex4g 2591 | . 2 |
18 | 14, 17 | bitrd 177 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wceq 1243 wex 1381 wcel 1393 cop 3378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 ax-pr 3944 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: opbrop 4419 ovi3 5637 dfplpq2 6452 dfmpq2 6453 enq0breq 6534 |
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