Metamath Proof Explorer


Theorem elpwg

Description: Membership in a power class. Theorem 86 of Suppes p. 47. See also elpw2g . (Contributed by NM, 6-Aug-2000) (Proof shortened by BJ, 31-Dec-2023)

Ref Expression
Assertion elpwg AVA𝒫BAB

Proof

Step Hyp Ref Expression
1 sseq1 x=AxBAB
2 df-pw 𝒫B=x|xB
3 1 2 elab2g AVA𝒫BAB