Theorem eqbrtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 17-Sep-2004)

	Ref	Expression
Hypotheses	eqbrtrrid.1	$$⊢B=A$$
	eqbrtrrid.2	$$⊢\phi \to BRC$$
Assertion	eqbrtrrid	$$⊢\phi \to ARC$$

Proof

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