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Metamath Proof Explorer

Theorem breqtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

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

Proof

Step Hyp Ref Expression
1 breqtrrdi.1 ⊢ φ → A R B
2 breqtrrdi.2 ⊢ C = B
3 2 eqcomi ⊢ B = C
4 1 3 breqtrdi ⊢ φ → A R C