Theorem eleqtri

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

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

Proof

Step	Hyp	Ref	Expression
1		eleqtri.1	$$⊢A\in B$$
2		eleqtri.2	$$⊢B=C$$
3	2	eleq2i	$$⊢A\in B\leftrightarrow A\in C$$
4	1 3	mpbi	$$⊢A\in C$$