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Metamath Proof Explorer

Theorem eqbrtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006)

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

Proof

Step Hyp Ref Expression
1 eqbrtrrdi.1 ⊢ φ → B = A
2 eqbrtrrdi.2 ⊢ B R C
3 1 eqcomd ⊢ φ → A = B
4 3 2 eqbrtrdi ⊢ φ → A R C