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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 3506 | . 2 | |
2 | 3simpa 963 | . . . . 5 | |
3 | 2 | con3i 606 | . . . 4 |
4 | 3 | alrimiv 1830 | . . 3 |
5 | abeq0 3363 | . . 3 | |
6 | 4, 5 | sylibr 133 | . 2 |
7 | 1, 6 | syl5eq 2162 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 w3a 947 wal 1314 wceq 1316 wcel 1465 cab 2103 cvv 2660 c0 3333 csn 3497 cpr 3498 cop 3500 |
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 588 ax-in2 589 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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-dif 3043 df-nul 3334 df-op 3506 |
This theorem is referenced by: opprc1 3697 opprc2 3698 ovprc 5774 |
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