Theorem eqeltrid

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

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

Proof

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