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 AV
Assertion pwid A𝒫A

Proof

Step Hyp Ref Expression
1 pwid.1 AV
2 pwidg AVA𝒫A
3 1 2 ax-mp A𝒫A