Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  opeq2i Structured version   Unicode version

Theorem opeq2i 3990
 Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1
Assertion
Ref Expression
opeq2i

Proof of Theorem opeq2i
StepHypRef Expression
1 opeq1i.1 . 2
2 opeq2 3987 . 2
31, 2ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wceq 1653  cop 3819 This theorem is referenced by:  fnressn  5920  fressnfv  5922  seqomlem1  6709  recmulnq  8843  addresr  9015  seqval  11336  ids1  11753  wrdeqs1cat  11791  ressinbas  13527  oduval  14559  efgi0  15354  efgi1  15355  vrgpinv  15403  frgpnabllem1  15486  zlmval  16799  vdgr1c  21678  avril1  21759  ginvsn  21939  nvop  22168  phop  22321  wfrlem14  25553  swrdccat3a  28239  bnj601  29353  tgrpset  31604  erngset  31659  erngset-rN  31667 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825
 Copyright terms: Public domain W3C validator