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Metamath Proof Explorer

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