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Metamath Proof Explorer

Theorem breqtrdi

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

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

Proof

Step Hyp Ref Expression
1 breqtrdi.1 ⊢ φ → A R B
2 breqtrdi.2 ⊢ B = C
3 eqid ⊢ A = A
4 1 3 2 3brtr3g ⊢ φ → A R C