Theorem breqtri

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

	Ref	Expression
Hypotheses	breqtr.1	$$⊢ARB$$
	breqtr.2	$$⊢B=C$$
Assertion	breqtri	$$⊢ARC$$

Proof

Step	Hyp	Ref	Expression
1		breqtr.1	$$⊢ARB$$
2		breqtr.2	$$⊢B=C$$
3	2	breq2i	$$⊢ARB\leftrightarrow ARC$$
4	1 3	mpbi	$$⊢ARC$$