Metamath Proof Explorer

Theorem pwidg

Description: A set is an element of its power set. (Contributed by Stefan O'Rear, 1-Feb-2015)

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

Proof

Step Hyp Ref Expression
1 ssid 
 |-  A C_ A
2 elpwg 
 |-  ( A e. V -> ( A e. ~P A <-> A C_ A ) )
3 1 2 mpbiri 
 |-  ( A e. V -> A e. ~P A )