Theorem eqeltrrdi

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

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

Proof

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