Theorem eqbrtrrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrrd.1	$$⊢\phi \to A=B$$
2		eqbrtrrd.2	$$⊢\phi \to ARC$$
3	1	eqcomd	$$⊢\phi \to B=A$$
4	3 2	eqbrtrd	$$⊢\phi \to BRC$$