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Theorem breqi 3851
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 3847 . 2  |-  ( R  =  S  ->  ( A R B  <->  A S B ) )
31, 2ax-mp 7 1  |-  ( A R B  <->  A S B )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    = wceq 1289   class class class wbr 3845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-cleq 2081  df-clel 2084  df-br 3846
This theorem is referenced by:  f1ompt  5450  brtpos2  6016  tfrexlem  6099  brdifun  6319  ltpiord  6878  ltxrlt  7552  ltxr  9246
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