Theorem pwid

Description: A set is a member of its power class. Theorem 87 of Suppes p. 47. (Contributed by NM, 5-Aug-1993)

	Ref	Expression
Hypothesis	pwid.1	$$⊢A\in \mathrm{V}$$
Assertion	pwid	$$⊢A\in 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		pwid.1	$$⊢A\in \mathrm{V}$$
2		pwidg	$$⊢A\in \mathrm{V}\to A\in 𝒫A$$
3	1 2	ax-mp	$$⊢A\in 𝒫A$$