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Mirrors > Home > ILE Home > Th. List > opeq12 | Unicode version |
Description: Equality theorem for ordered pairs. (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
opeq12 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1 3713 |
. 2
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2 | opeq2 3714 |
. 2
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3 | 1, 2 | sylan9eq 2193 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
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 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 |
This theorem is referenced by: opeq12i 3718 opeq12d 3721 cbvopab 4007 opth 4167 copsex2t 4175 copsex2g 4176 relop 4697 funopg 5165 fsn 5600 fnressn 5614 cbvoprab12 5853 eqopi 6078 f1o2ndf1 6133 tposoprab 6185 brecop 6527 th3q 6542 ecovcom 6544 ecovicom 6545 ecovass 6546 ecoviass 6547 ecovdi 6548 ecovidi 6549 xpf1o 6746 1qec 7220 enq0sym 7264 addnq0mo 7279 mulnq0mo 7280 addnnnq0 7281 mulnnnq0 7282 distrnq0 7291 mulcomnq0 7292 addassnq0 7294 addsrmo 7575 mulsrmo 7576 addsrpr 7577 mulsrpr 7578 axcnre 7713 fsumcnv 11238 eucalgval2 11770 |
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