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 ∈ V
Assertion	pwid	⊢ 𝐴 ∈ 𝒫 𝐴

Proof

Step	Hyp	Ref	Expression
1		pwid.1	⊢ 𝐴 ∈ V
2		pwidg	⊢ ( 𝐴 ∈ V → 𝐴 ∈ 𝒫 𝐴 )
3	1 2	ax-mp	⊢ 𝐴 ∈ 𝒫 𝐴