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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 3551 | . 2 | |
4 | 1, 2, 3 | mp2an 402 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1243 cop 3378 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-sn 3381 df-pr 3382 df-op 3384 |
This theorem is referenced by: addpinq1 6562 genipv 6607 ltexpri 6711 recexpr 6736 cauappcvgprlemladdru 6754 cauappcvgprlemladdrl 6755 cauappcvgpr 6760 caucvgprlemcl 6774 caucvgprlemladdrl 6776 caucvgpr 6780 caucvgprprlemval 6786 caucvgprprlemnbj 6791 caucvgprprlemmu 6793 caucvgprprlemclphr 6803 caucvgprprlemaddq 6806 caucvgprprlem1 6807 caucvgprprlem2 6808 caucvgsr 6886 pitonnlem1 6921 axi2m1 6949 axcaucvg 6974 |
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