Metamath Proof Explorer

Theorem elpwgdedVD

Description: Membership in a power class. Theorem 86 of Suppes p. 47. Derived from elpwg . In form of VD deduction with ph and ps as variable virtual hypothesis collections based on Mario Carneiro's metavariable concept. elpwgded is elpwgdedVD using conventional notation. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Hypotheses elpwgdedVD.1 φ A V
elpwgdedVD.2 ψ A B
Assertion elpwgdedVD φ ψ A 𝒫 B


Step Hyp Ref Expression
1 elpwgdedVD.1 φ A V
2 elpwgdedVD.2 ψ A B
3 elpwg A V A 𝒫 B A B
4 3 biimpar A V A B A 𝒫 B
5 1 2 4 el12 φ ψ A 𝒫 B