Theorem eqeltrdi

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

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

Proof

Step	Hyp	Ref	Expression
1		eqeltrdi.1	$$⊢\phi \to A=B$$
2		eqeltrdi.2	$$⊢B\in C$$
3	2	a1i	$$⊢\phi \to B\in C$$
4	1 3	eqeltrd	$$⊢\phi \to A\in C$$