Metamath Proof Explorer

Theorem neufal

Description: There does not exist exactly one set such that F. is true. (Contributed by Anthony Hart, 13-Sep-2011)

Ref Expression
Assertion neufal 
|- -. E! x F.

Proof

Step Hyp Ref Expression
1 nexfal 
 |-  -. E. x F.
2 euex 
 |-  ( E! x F. -> E. x F. )
3 1 2 mto 
 |-  -. E! x F.