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Metamath Proof Explorer

Theorem eqbrtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004)

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

Proof

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