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Theorem opeq2i 4773
 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 4769 . 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 1538  ⟨cop 4534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-un 3888  df-sn 4529  df-pr 4531  df-op 4535 This theorem is referenced by:  fnressn  6907  fressnfv  6909  wfrlem14  7969  seqomlem1  8087  recmulnq  10393  addresr  10567  seqval  13395  ids1  13962  pfx1  14076  pfxccatpfx2  14110  ressinbas  16572  oduval  17752  mgmnsgrpex  18108  sgrpnmndex  18109  efgi0  18859  efgi1  18860  vrgpinv  18908  frgpnabllem1  19007  mat1dimid  21120  uspgr1v1eop  27083  wlk2v2e  27986  avril1  28292  nvop  28503  phop  28645  bnj601  32368  tgrpset  38192  erngset  38247  erngset-rN  38255  zlmodzxzadd  44928  lmod1  45067  lmod1zr  45068  zlmodzxzequa  45071  zlmodzxzequap  45074
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