Theorem eleqtrrid

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

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

Proof

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