Metamath Proof Explorer

Theorem snnz

Description: The singleton of a set is not empty. (Contributed by NM, 10-Apr-1994)

Ref Expression
Hypothesis snnz.1 
|- A e. _V
Assertion snnz 
|- { A } =/= (/)

Proof

Step Hyp Ref Expression
1 snnz.1 
 |-  A e. _V
2 snnzg 
 |-  ( A e. _V -> { A } =/= (/) )
3 1 2 ax-mp 
 |-  { A } =/= (/)