Theorem breqtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

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

Proof

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