Theorem eleqtrrdi

Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005)

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

Proof

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