Theorem breqtrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 11-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		breqtrdi.1	$$⊢\phi \to ARB$$
2		breqtrdi.2	$$⊢B=C$$
3		eqid	$$⊢A=A$$
4	1 3 2	3brtr3g	$$⊢\phi \to ARC$$