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Theorem unnf 26162
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 26161 . 2  |-  -.  E. x  F.
2 euex 2306 . 2  |-  ( E! x  F.  ->  E. x  F.  )
31, 2mto 170 1  |-  -.  E! x  F.
Colors of variables: wff set class
Syntax hints:   -. wn 3    F. wfal 1327   E.wex 1551   E!weu 2283
This theorem is referenced by:  unqsym1  26180
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-fal 1330  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287
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