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Mirrors > Home > ILE Home > Th. List > opprc | Unicode version |
Description: Expansion of an ordered pair when either member is a proper class. (Contributed by Mario Carneiro, 26-Apr-2015.) |
Ref | Expression |
---|---|
opprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-op 3590 | . 2 | |
2 | 3simpa 989 | . . . . 5 | |
3 | 2 | con3i 627 | . . . 4 |
4 | 3 | alrimiv 1867 | . . 3 |
5 | abeq0 3444 | . . 3 | |
6 | 4, 5 | sylibr 133 | . 2 |
7 | 1, 6 | eqtrid 2215 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 973 wal 1346 wceq 1348 wcel 2141 cab 2156 cvv 2730 c0 3414 csn 3581 cpr 3582 cop 3584 |
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-in1 609 ax-in2 610 ax-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-fal 1354 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-dif 3123 df-nul 3415 df-op 3590 |
This theorem is referenced by: opprc1 3785 opprc2 3786 ovprc 5886 |
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