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Theorem unnf 26069
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 26068 . 2  |-  -.  E. x  F.
2 euex 2285 . 2  |-  ( E! x  F.  ->  E. x  F.  )
31, 2mto 169 1  |-  -.  E! x  F.
Colors of variables: wff set class
Syntax hints:   -. wn 3    F. wfal 1323   E.wex 1547   E!weu 2262
This theorem is referenced by:  unqsym1  26087
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-fal 1326  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266
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