Theorem eqbrtrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 12-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrdi.1	$$⊢\phi \to A=B$$
2		eqbrtrdi.2	$$⊢BRC$$
3	1	breq1d	$$⊢\phi \to \left(ARC\leftrightarrow BRC\right)$$
4	2 3	mpbiri	$$⊢\phi \to ARC$$