Theorem eleq1

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

	Ref	Expression
Assertion	eleq1	$$⊢A=B\to \left(A\in C\leftrightarrow B\in C\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A=B\to A=B$$
2	1	eleq1d	$$⊢A=B\to \left(A\in C\leftrightarrow B\in C\right)$$