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Theorem unnf 32743
Description: There does not exist exactly one set, such that is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
unnf ¬ ∃!𝑥

Proof of Theorem unnf
StepHypRef Expression
1 nextf 32742 . 2 ¬ ∃𝑥
2 euex 2642 . 2 (∃!𝑥⊥ → ∃𝑥⊥)
31, 2mto 188 1 ¬ ∃!𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wfal 1636  wex 1852  ∃!weu 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057
This theorem depends on definitions:  df-bi 197  df-tru 1634  df-fal 1637  df-ex 1853  df-eu 2622
This theorem is referenced by:  unqsym1  32761
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