Theorem eleqtrrd

Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004)

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

Proof

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