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Mirrors > Home > ILE Home > Th. List > eqopab2b | Unicode version |
Description: Equivalence of ordered pair abstraction equality and biconditional. (Contributed by Mario Carneiro, 4-Jan-2017.) |
Ref | Expression |
---|---|
eqopab2b |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssopab2b 4261 | . . 3 | |
2 | ssopab2b 4261 | . . 3 | |
3 | 1, 2 | anbi12i 457 | . 2 |
4 | eqss 3162 | . 2 | |
5 | 2albiim 1481 | . 2 | |
6 | 3, 4, 5 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wceq 1348 wss 3121 copab 4049 |
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 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-14 2144 ax-ext 2152 ax-sep 4107 ax-pow 4160 ax-pr 4194 |
This theorem depends on definitions: df-bi 116 df-3an 975 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-pw 3568 df-sn 3589 df-pr 3590 df-op 3592 df-opab 4051 |
This theorem is referenced by: (None) |
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