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Theorem opeq2i 4075
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 4072 . 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 1369   <.cop 3895
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2577  df-rab 2736  df-v 2986  df-dif 3343  df-un 3345  df-in 3347  df-ss 3354  df-nul 3650  df-if 3804  df-sn 3890  df-pr 3892  df-op 3896
This theorem is referenced by:  fnressn  5906  fressnfv  5908  seqomlem1  6917  recmulnq  9145  addresr  9317  seqval  11829  ids1  12301  wrdeqs1cat  12381  swrdccat3a  12397  ressinbas  14246  oduval  15312  efgi0  16229  efgi1  16230  vrgpinv  16278  frgpnabllem1  16363  vdgr1c  23587  avril1  23668  ginvsn  23848  nvop  24077  phop  24230  signstfveq0  26990  wfrlem14  27749  clwlkfoclwwlk  30530  zlmodzxzadd  30767  mat1dimid  30882  lmod1  31046  lmod1zr  31047  zlmodzxzequa  31050  zlmodzxzequap  31053  bnj601  31925  tgrpset  34401  erngset  34456  erngset-rN  34464
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