Metamath Proof Explorer


Theorem breqtrri

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 1-Aug-1999)

Ref Expression
Hypotheses breqtrr.1 ⊢ A R B
breqtrr.2 ⊢ C = B
Assertion breqtrri ⊢ A R C

Proof

Step Hyp Ref Expression
1 breqtrr.1 ⊢ A R B
2 breqtrr.2 ⊢ C = B
3 2 eqcomi ⊢ B = C
4 1 3 breqtri ⊢ A R C