Metamath Proof Explorer

Theorem snidb

Description: A class is a set iff it is a member of its singleton. (Contributed by NM, 5-Apr-2004)

Ref Expression
Assertion snidb 
|- ( A e. _V <-> A e. { A } )

Proof

Step Hyp Ref Expression
1 snidg 
 |-  ( A e. _V -> A e. { A } )
2 elex 
 |-  ( A e. { A } -> A e. _V )
3 1 2 impbii 
 |-  ( A e. _V <-> A e. { A } )