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Metamath Proof Explorer

Theorem breqtrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999)

Ref Expression
Hypotheses breqtrid.1 ⊢ A R B
breqtrid.2 ⊢ φ → B = C
Assertion breqtrid ⊢ φ → A R C

Proof

Step Hyp Ref Expression
1 breqtrid.1 ⊢ A R B
2 breqtrid.2 ⊢ φ → B = C
3 1 a1i ⊢ φ → A R B
4 3 2 breqtrd ⊢ φ → A R C