Metamath Proof Explorer

Theorem pwidg

Description: A set is an element of its power set. (Contributed by Stefan O'Rear, 1-Feb-2015) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion pwidg 
|- ( A e. V -> A e. ~P A )

Proof

Step Hyp Ref Expression
1 elex 
 |-  ( A e. V -> A e. _V )
2 ssidd 
 |-  ( A e. V -> A C_ A )
3 1 2 elpwd 
 |-  ( A e. V -> A e. ~P A )