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Theorem opeq2i 3745
 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 3742 . 2 (𝐴 = 𝐵 → ⟨𝐶, 𝐴⟩ = ⟨𝐶, 𝐵⟩)
31, 2ax-mp 5 1 𝐶, 𝐴⟩ = ⟨𝐶, 𝐵
 Colors of variables: wff set class Syntax hints:   = wceq 1335  ⟨cop 3563 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569 This theorem is referenced by:  fnressn  5652  fressnfv  5653  nqprlu  7461  suplocexpr  7639  addresr  7751  iseqvalcbv  10349
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