Theorem eqeltri

Description: Substitution of equal classes into membership relation. (Contributed by NM, 21-Jun-1993)

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

Proof

Step	Hyp	Ref	Expression
1		eqeltri.1	$$⊢A=B$$
2		eqeltri.2	$$⊢B\in C$$
3	1	eleq1i	$$⊢A\in C\leftrightarrow B\in C$$
4	2 3	mpbir	$$⊢A\in C$$