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Metamath Proof Explorer

Theorem eqbrtrrd

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

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

Proof

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