Metamath Proof Explorer


Theorem eqbrtrri

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

Ref Expression
Hypotheses eqbrtrr.1
|- A = B
eqbrtrr.2
|- A R C
Assertion eqbrtrri
|- B R C

Proof

Step Hyp Ref Expression
1 eqbrtrr.1
 |-  A = B
2 eqbrtrr.2
 |-  A R C
3 1 eqcomi
 |-  B = A
4 3 2 eqbrtri
 |-  B R C