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Metamath Proof Explorer

Theorem breq12

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

Ref Expression
Assertion breq12 ⊢ A = B ∧ C = D → A R C ↔ B R D

Proof

Step Hyp Ref Expression
1 breq1 ⊢ A = B → A R C ↔ B R C
2 breq2 ⊢ C = D → B R C ↔ B R D
3 1 2 sylan9bb ⊢ A = B ∧ C = D → A R C ↔ B R D