Theorem pwidg

Description: A set is an element of its power set. (Contributed by Stefan O'Rear, 1-Feb-2015) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	Ref	Expression
Assertion	pwidg	$$⊢A\in V\to A\in 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		elex	$$⊢A\in V\to A\in \mathrm{V}$$
2		ssidd	$$⊢A\in V\to A\subseteq A$$
3	1 2	elpwd	$$⊢A\in V\to A\in 𝒫A$$