Theorem eleqtrri

Description: Substitution of equal classes into membership relation. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypotheses	eleqtrri.1	$$⊢A\in B$$
	eleqtrri.2	$$⊢C=B$$
Assertion	eleqtrri	$$⊢A\in C$$

Proof

Step	Hyp	Ref	Expression
1		eleqtrri.1	$$⊢A\in B$$
2		eleqtrri.2	$$⊢C=B$$
3	2	eqcomi	$$⊢B=C$$
4	1 3	eleqtri	$$⊢A\in C$$