Metamath Proof Explorer

Theorem velpw

Description: Setvar variable membership in a power class. (Contributed by David A. Wheeler, 8-Dec-2018)

Ref Expression
Assertion velpw 
|- ( x e. ~P A <-> x C_ A )

Proof

Step Hyp Ref Expression
1 vex 
 |-  x e. _V
2 1 elpw 
 |-  ( x e. ~P A <-> x C_ A )