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	$$⊢BRC$$
Assertion	eqbrtri	$$⊢ARC$$

Proof

Step	Hyp	Ref	Expression
1		eqbrtr.1	$$⊢A=B$$
2		eqbrtr.2	$$⊢BRC$$
3	1	breq1i	$$⊢ARC\leftrightarrow BRC$$
4	2 3	mpbir	$$⊢ARC$$