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Theorem opeq1i 4798
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 4795 . 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 1528  cop 4563
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-3an 1081  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-nfc 2960  df-rab 3144  df-v 3494  df-dif 3936  df-un 3938  df-in 3940  df-ss 3949  df-nul 4289  df-if 4464  df-sn 4558  df-pr 4560  df-op 4564
This theorem is referenced by:  axi2m1  10569  s3tpop  14259  2strstr1  16593  2strop1  16595  grpbasex  16601  grpplusgx  16602  mat1dimelbas  21008  mat1dim0  21010  mat1dimid  21011  mat1dimscm  21012  mat1dimmul  21013  indistpsx  21546  setsiedg  26748  cusgrsize  27163  mapfzcons  39191
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