Theorem breqtrrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

	Ref	Expression
Hypotheses	breqtrrd.1	$$⊢\phi \to ARB$$
	breqtrrd.2	$$⊢\phi \to C=B$$
Assertion	breqtrrd	$$⊢\phi \to ARC$$

Proof

Step	Hyp	Ref	Expression
1		breqtrrd.1	$$⊢\phi \to ARB$$
2		breqtrrd.2	$$⊢\phi \to C=B$$
3	2	eqcomd	$$⊢\phi \to B=C$$
4	1 3	breqtrd	$$⊢\phi \to ARC$$