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Metamath Proof Explorer

Theorem neutru

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

Ref Expression
Assertion neutru 
|- -. E! x T.

Proof

Step Hyp Ref Expression
1 nexntru 
 |-  -. E. x -. T.
2 eunex 
 |-  ( E! x T. -> E. x -. T. )
3 1 2 mto 
 |-  -. E! x T.