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Theorem opeq2i 4206
Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1  |-  A  =  B
Assertion
Ref Expression
opeq2i  |-  <. C ,  A >.  =  <. C ,  B >.

Proof of Theorem opeq2i
StepHypRef Expression
1 opeq1i.1 . 2  |-  A  =  B
2 opeq2 4203 . 2  |-  ( A  =  B  ->  <. C ,  A >.  =  <. C ,  B >. )
31, 2ax-mp 5 1  |-  <. C ,  A >.  =  <. C ,  B >.
Colors of variables: wff setvar class
Syntax hints:    = wceq 1383   <.cop 4020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021
This theorem is referenced by:  fnressn  6068  fressnfv  6070  seqomlem1  7117  recmulnq  9345  addresr  9518  seqval  12097  ids1  12588  wrdeqs1cat  12679  swrdccat3a  12698  ressinbas  14570  oduval  15634  mgmnsgrpex  15923  sgrpnmndex  15924  efgi0  16612  efgi1  16613  vrgpinv  16661  frgpnabllem1  16751  mat1dimid  18849  clwlkfoclwwlk  24717  vdgr1c  24777  avril1  25043  ginvsn  25223  nvop  25452  phop  25605  signstfveq0  28407  wfrlem14  29331  zlmodzxzadd  32680  lmod1  32828  lmod1zr  32829  zlmodzxzequa  32832  zlmodzxzequap  32835  bnj601  33711  tgrpset  36211  erngset  36266  erngset-rN  36274
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