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Theorem breqd 3766
Description: Equality deduction for a binary relation. (Contributed by NM, 29-Oct-2011.)
Hypothesis
Ref Expression
breq1d.1 (φA = B)
Assertion
Ref Expression
breqd (φ → (𝐶A𝐷𝐶B𝐷))

Proof of Theorem breqd
StepHypRef Expression
1 breq1d.1 . 2 (φA = B)
2 breq 3757 . 2 (A = B → (𝐶A𝐷𝐶B𝐷))
31, 2syl 14 1 (φ → (𝐶A𝐷𝐶B𝐷))
Colors of variables: wff set class
Syntax hints:  wi 4  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:  breq123d  3769  sbcbr12g  3805  sprmpt2  5798
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