Theorem eleqtrid

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

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

Proof

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