Metamath Proof Explorer


Theorem breq2i

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

Ref Expression
Hypothesis breq1i.1 ⊢ A = B
Assertion breq2i ⊢ C R A ↔ C R B

Proof

Step Hyp Ref Expression
1 breq1i.1 ⊢ A = B
2 breq2 ⊢ A = B → C R A ↔ C R B
3 1 2 ax-mp ⊢ C R A ↔ C R B