Theorem eqbrtrid

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

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrid.1	$$⊢A=B$$
2		eqbrtrid.2	$$⊢\phi \to BRC$$
3		eqid	$$⊢C=C$$
4	2 1 3	3brtr4g	$$⊢\phi \to ARC$$