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Theorem unnf 25405
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 25404 . 2  |-  -.  E. x  F.
2 euex 2232 . 2  |-  ( E! x  F.  ->  E. x  F.  )
31, 2mto 167 1  |-  -.  E! x  F.
Colors of variables: wff set class
Syntax hints:   -. wn 3    F. wfal 1317   E.wex 1541   E!weu 2209
This theorem is referenced by:  unqsym1  25423
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-fal 1320  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2213
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