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Theorem breqi 4011
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 4007 . 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 105    = wceq 1353   class class class wbr 4005
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-cleq 2170  df-clel 2173  df-br 4006
This theorem is referenced by:  f1ompt  5669  brtpos2  6254  tfrexlem  6337  brdifun  6564  ltpiord  7320  ltxrlt  8025  ltxr  9777  xmeterval  14020
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