Theorem eqbrtri

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

	Ref	Expression
Hypotheses	eqbrtr.1	|- A = B
	eqbrtr.2	|- B R C
Assertion	eqbrtri	|- A R C

Proof

Step	Hyp	Ref	Expression
1		eqbrtr.1	|- A = B
2		eqbrtr.2	|- B R C
3	1	breq1i	|- ( A R C <-> B R C )
4	2 3	mpbir	|- A R C