Theorem eqeltrrid

Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)

	Ref	Expression
Hypotheses	eqeltrrid.1	$$⊢B=A$$
	eqeltrrid.2	$$⊢\phi \to B\in C$$
Assertion	eqeltrrid	$$⊢\phi \to A\in C$$

Proof

Step	Hyp	Ref	Expression
1		eqeltrrid.1	$$⊢B=A$$
2		eqeltrrid.2	$$⊢\phi \to B\in C$$
3	1	eqcomi	$$⊢A=B$$
4	3 2	eqeltrid	$$⊢\phi \to A\in C$$