Theorem snid

Description: A set is a member of its singleton. Part of Theorem 7.6 of Quine p. 49. (Contributed by NM, 31-Dec-1993)

	Ref	Expression
Hypothesis	snid.1	|- A e. _V
Assertion	snid	|- A e. { A }

Proof

Step	Hyp	Ref	Expression
1		snid.1	|- A e. _V
2		snidb	|- ( A e. _V <-> A e. { A } )
3	1 2	mpbi	|- A e. { A }