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Metamath Proof Explorer

Theorem breqtri

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999)

Ref Expression
Hypotheses breqtr.1 ⊢ A R B
breqtr.2 ⊢ B = C
Assertion breqtri ⊢ A R C

Proof

Step Hyp Ref Expression
1 breqtr.1 ⊢ A R B
2 breqtr.2 ⊢ B = C
3 2 breq2i ⊢ A R B ↔ A R C
4 1 3 mpbi ⊢ A R C