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Theorem breqi 3761
 Description: Equality inference for binary relations. (Contributed by NM, 19-Feb-2005.)
Hypothesis
Ref Expression
breqi.1 𝑅 = 𝑆
Assertion
Ref Expression
breqi (A𝑅BA𝑆B)

Proof of Theorem breqi
StepHypRef Expression
1 breqi.1 . 2 𝑅 = 𝑆
2 breq 3757 . 2 (𝑅 = 𝑆 → (A𝑅BA𝑆B))
31, 2ax-mp 7 1 (A𝑅BA𝑆B)
 Colors of variables: wff set class Syntax hints:   ↔ wb 98   = wceq 1242   class class class wbr 3755 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-clel 2033  df-br 3756 This theorem is referenced by:  f1ompt  5263  brtpos2  5807  tfrexlem  5889  brdifun  6069  ltpiord  6303  ltxrlt  6862  ltxr  8445
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