Metamath Proof Explorer


Theorem breq2d

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

Ref Expression
Hypothesis breq1d.1 ⊢ φ → A = B
Assertion breq2d ⊢ φ → C R A ↔ C R B

Proof

Step Hyp Ref Expression
1 breq1d.1 ⊢ φ → A = B
2 breq2 ⊢ A = B → C R A ↔ C R B
3 1 2 syl ⊢ φ → C R A ↔ C R B