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Theorem opeq1i 4205
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 4202 . 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 1383   <.cop 4020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-11 1828  ax-12 1840  ax-13 1985  ax-ext 2421
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 976  df-tru 1386  df-ex 1600  df-nf 1604  df-sb 1727  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2593  df-rab 2802  df-v 3097  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3771  df-if 3927  df-sn 4015  df-pr 4017  df-op 4021
This theorem is referenced by:  axi2m1  9539  strlemor1  14706  grpbasex  14722  grpplusgx  14723  mat1dimelbas  18951  mat1dim0  18953  mat1dimid  18954  mat1dimscm  18955  mat1dimmul  18956  indistpsx  19489  mapfzcons  30624  uhgrepe  32332
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