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Metamath Proof Explorer

Theorem breqtrrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

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

Proof

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