Theorem eleq2

Description: Equality implies equivalence of membership. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 20-Nov-2019)

	Ref	Expression
Assertion	eleq2	$$⊢A=B\to \left(C\in A\leftrightarrow C\in B\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A=B\to A=B$$
2	1	eleq2d	$$⊢A=B\to \left(C\in A\leftrightarrow C\in B\right)$$