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Theorem opeq1i 3672
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 3669 . 2  |-  ( A  =  B  ->  <. A ,  C >.  =  <. B ,  C >. )
31, 2ax-mp 7 1  |-  <. A ,  C >.  =  <. B ,  C >.
Colors of variables: wff set class
Syntax hints:    = wceq 1312   <.cop 3494
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095
This theorem depends on definitions:  df-bi 116  df-3an 945  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-un 3039  df-sn 3497  df-pr 3498  df-op 3500
This theorem is referenced by:  caucvgsrlemfv  7527  caucvgsr  7538  pitonnlem1  7574  axi2m1  7604  axcaucvg  7629  ennnfonelem1  11759  2strstr1g  11899  2strop1g  11901
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