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Theorem opeq1i 4343
 Description: Equality inference for ordered pairs. (Contributed by NM, 16-Dec-2006.)
Hypothesis
Ref Expression
opeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
opeq1i 𝐴, 𝐶⟩ = ⟨𝐵, 𝐶

Proof of Theorem opeq1i
StepHypRef Expression
1 opeq1i.1 . 2 𝐴 = 𝐵
2 opeq1 4340 . 2 (𝐴 = 𝐵 → ⟨𝐴, 𝐶⟩ = ⟨𝐵, 𝐶⟩)
31, 2ax-mp 5 1 𝐴, 𝐶⟩ = ⟨𝐵, 𝐶
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ⟨cop 4131 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132 This theorem is referenced by:  axi2m1  9859  s3tpop  13504  strlemor1  15796  2strstr1  15812  2strop1  15814  grpbasex  15819  grpplusgx  15820  mat1dimelbas  20096  mat1dim0  20098  mat1dimid  20099  mat1dimscm  20100  mat1dimmul  20101  indistpsx  20624  uhgrstrrepe  25745  mapfzcons  36297  cusgrsize  40670
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