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Theorem breqi 3935
Description: Equality inference for binary relations. (Contributed by NM, 19-Feb-2005.)
Hypothesis
Ref Expression
breqi.1  |-  R  =  S
Assertion
Ref Expression
breqi  |-  ( A R B  <->  A S B )

Proof of Theorem breqi
StepHypRef Expression
1 breqi.1 . 2  |-  R  =  S
2 breq 3931 . 2  |-  ( R  =  S  ->  ( A R B  <->  A S B ) )
31, 2ax-mp 5 1  |-  ( A R B  <->  A S B )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    = wceq 1331   class class class wbr 3929
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-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-cleq 2132  df-clel 2135  df-br 3930
This theorem is referenced by:  f1ompt  5571  brtpos2  6148  tfrexlem  6231  brdifun  6456  ltpiord  7134  ltxrlt  7837  ltxr  9569  xmeterval  12614
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