Metamath Proof Explorer

Theorem sels

Description: If a class is a set, then it is a member of a set. (Contributed by BJ, 3-Apr-2019)

Ref Expression
Assertion sels 
|- ( A e. V -> E. x A e. x )

Proof

Step Hyp Ref Expression
1 snidg 
 |-  ( A e. V -> A e. { A } )
2 snex 
 |-  { A } e. _V
3 eleq2 
 |-  ( x = { A } -> ( A e. x <-> A e. { A } ) )
4 2 3 spcev 
 |-  ( A e. { A } -> E. x A e. x )
5 1 4 syl 
 |-  ( A e. V -> E. x A e. x )