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Theorem opeq2i 4217
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 4214 . 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 1379   <.cop 4033
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034
This theorem is referenced by:  fnressn  6074  fressnfv  6076  seqomlem1  7116  recmulnq  9343  addresr  9516  seqval  12087  ids1  12575  wrdeqs1cat  12666  swrdccat3a  12685  ressinbas  14554  oduval  15620  efgi0  16553  efgi1  16554  vrgpinv  16602  frgpnabllem1  16692  mat1dimid  18783  clwlkfoclwwlk  24618  vdgr1c  24678  avril1  24944  ginvsn  25124  nvop  25353  phop  25506  signstfveq0  28285  wfrlem14  29209  zlmodzxzadd  32242  lmod1  32391  lmod1zr  32392  zlmodzxzequa  32395  zlmodzxzequap  32398  bnj601  33274  tgrpset  35758  erngset  35813  erngset-rN  35821
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