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Theorem unnf 31066
Description: There does not exist exactly one set, such that F. is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
unnf  |-  -.  E! x F.

Proof of Theorem unnf
StepHypRef Expression
1 nextf 31065 . 2  |-  -.  E. x F.
2 euex 2291 . 2  |-  ( E! x F.  ->  E. x F.  )
31, 2mto 180 1  |-  -.  E! x F.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   F. wfal 1443   E.wex 1660   E!weu 2266
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795
This theorem depends on definitions:  df-bi 189  df-tru 1441  df-fal 1444  df-ex 1661  df-eu 2270
This theorem is referenced by:  unqsym1  31084
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