Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > opeq12 | Unicode version |
Description: Equality theorem for ordered pairs. (Contributed by NM, 28-May-1995.) |
Ref | Expression |
---|---|
opeq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opeq1 3700 | . 2 | |
2 | opeq2 3701 | . 2 | |
3 | 1, 2 | sylan9eq 2190 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 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: opeq12i 3705 opeq12d 3708 cbvopab 3994 opth 4154 copsex2t 4162 copsex2g 4163 relop 4684 funopg 5152 fsn 5585 fnressn 5599 cbvoprab12 5838 eqopi 6063 f1o2ndf1 6118 tposoprab 6170 brecop 6512 th3q 6527 ecovcom 6529 ecovicom 6530 ecovass 6531 ecoviass 6532 ecovdi 6533 ecovidi 6534 xpf1o 6731 1qec 7189 enq0sym 7233 addnq0mo 7248 mulnq0mo 7249 addnnnq0 7250 mulnnnq0 7251 distrnq0 7260 mulcomnq0 7261 addassnq0 7263 addsrmo 7544 mulsrmo 7545 addsrpr 7546 mulsrpr 7547 axcnre 7682 fsumcnv 11199 eucalgval2 11723 |
Copyright terms: Public domain | W3C validator |