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 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elex	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ V )
2		ssidd	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ⊆ 𝐴 )
3	1 2	elpwd	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴 )