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 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ssid	⊢ 𝐴 ⊆ 𝐴
2		elpwg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∈ 𝒫 𝐴 ↔ 𝐴 ⊆ 𝐴 ) )
3	1 2	mpbiri	⊢ ( 𝐴 ∈ 𝑉 → 𝐴 ∈ 𝒫 𝐴 )