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Theorem opeq2i 3626
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 3623 . 2 (𝐴 = 𝐵 → ⟨𝐶, 𝐴⟩ = ⟨𝐶, 𝐵⟩)
31, 2ax-mp 7 1 𝐶, 𝐴⟩ = ⟨𝐶, 𝐵
Colors of variables: wff set class
Syntax hints:   = wceq 1289  cop 3449
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-sn 3452  df-pr 3453  df-op 3455
This theorem is referenced by:  fnressn  5483  fressnfv  5484  nqprlu  7106  addresr  7374  iseqvalcbv  9872
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