Theorem eleqtrdi

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

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

Proof

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