Theorem snidg

Description: A set is a member of its singleton. Part of Theorem 7.6 of Quine p. 49. (Contributed by NM, 28-Oct-2003)

	Ref	Expression
Assertion	snidg	$$⊢A\in V\to A\in \left\{A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢A=A$$
2		elsng	$$⊢A\in V\to \left(A\in \left\{A\right\}\leftrightarrow A=A\right)$$
3	1 2	mpbiri	$$⊢A\in V\to A\in \left\{A\right\}$$