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Metamath Proof Explorer

Theorem breq1d

Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996)

Ref Expression
Hypothesis breq1d.1 ⊢ φ → A = B
Assertion breq1d ⊢ φ → A R C ↔ B R C

Proof

Step Hyp Ref Expression
1 breq1d.1 ⊢ φ → A = B
2 breq1 ⊢ A = B → A R C ↔ B R C
3 1 2 syl ⊢ φ → A R C ↔ B R C