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Mirrors > Home > ILE Home > Th. List > opeq12i | Unicode version |
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.) (Proof shortened by Eric Schmidt, 4-Apr-2007.) |
Ref | Expression |
---|---|
opeq1i.1 | |
opeq12i.2 |
Ref | Expression |
---|---|
opeq12i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1i.1 | . 2 | |
2 | opeq12i.2 | . 2 | |
3 | opeq12 3702 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 cop 3525 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-un 3070 df-sn 3528 df-pr 3529 df-op 3531 |
This theorem is referenced by: addpinq1 7265 genipv 7310 ltexpri 7414 recexpr 7439 cauappcvgprlemladdru 7457 cauappcvgprlemladdrl 7458 cauappcvgpr 7463 caucvgprlemcl 7477 caucvgprlemladdrl 7479 caucvgpr 7483 caucvgprprlemval 7489 caucvgprprlemnbj 7494 caucvgprprlemmu 7496 caucvgprprlemclphr 7506 caucvgprprlemaddq 7509 caucvgprprlem1 7510 caucvgprprlem2 7511 caucvgsr 7603 pitonnlem1 7646 axi2m1 7676 axcaucvg 7701 |
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