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Mirrors > Home > ILE Home > Th. List > eqoprab2b | Unicode version |
Description: Equivalence of ordered pair abstraction subclass and biconditional. Compare eqopab2b 4251. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
eqoprab2b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssoprab2b 5890 | . . 3 | |
2 | ssoprab2b 5890 | . . 3 | |
3 | 1, 2 | anbi12i 456 | . 2 |
4 | eqss 3152 | . 2 | |
5 | 2albiim 1475 | . . . 4 | |
6 | 5 | albii 1457 | . . 3 |
7 | 19.26 1468 | . . 3 | |
8 | 6, 7 | bitri 183 | . 2 |
9 | 3, 4, 8 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1340 wceq 1342 wss 3111 coprab 5837 |
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 604 ax-in2 605 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 ax-setind 4508 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-fal 1348 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-ral 2447 df-v 2723 df-dif 3113 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-oprab 5840 |
This theorem is referenced by: mpo2eqb 5942 |
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