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Theorem breqd 4650
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 4641 . 2 (A = B → (CADCBD))
31, 2syl 15 1 (φ → (CADCBD))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176   = wceq 1642   class class class wbr 4639
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-cleq 2346  df-clel 2349  df-br 4640
This theorem is referenced by:  breq123d  4653  sbcbr12g  4686
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