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	$$⊢A\in \mathrm{V}$$
Assertion	snid	$$⊢A\in \left\{A\right\}$$

Proof

Step	Hyp	Ref	Expression
1		snid.1	$$⊢A\in \mathrm{V}$$
2		snidb	$$⊢A\in \mathrm{V}\leftrightarrow A\in \left\{A\right\}$$
3	1 2	mpbi	$$⊢A\in \left\{A\right\}$$