Theorem pwidg

Description: A set is an element of its power set. (Contributed by Stefan O'Rear, 1-Feb-2015)

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

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢A\subseteq A$$
2		elpwg	$$⊢A\in V\to \left(A\in 𝒫A\leftrightarrow A\subseteq A\right)$$
3	1 2	mpbiri	$$⊢A\in V\to A\in 𝒫A$$