Theorem snidb

Description: A class is a set iff it is a member of its singleton. (Contributed by NM, 5-Apr-2004)

	Ref	Expression
Assertion	snidb	$$⊢A\in \mathrm{V}\leftrightarrow A\in \left\{A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		snidg	$$⊢A\in \mathrm{V}\to A\in \left\{A\right\}$$
2		elex	$$⊢A\in \left\{A\right\}\to A\in \mathrm{V}$$
3	1 2	impbii	$$⊢A\in \mathrm{V}\leftrightarrow A\in \left\{A\right\}$$