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Theorem neufal 33641
Description: There does not exist exactly one set such that is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
neufal ¬ ∃!𝑥

Proof of Theorem neufal
StepHypRef Expression
1 nexfal 33640 . 2 ¬ ∃𝑥
2 euex 2659 . 2 (∃!𝑥⊥ → ∃𝑥⊥)
31, 2mto 198 1 ¬ ∃!𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wfal 1542  wex 1773  ∃!weu 2650
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789
This theorem depends on definitions:  df-bi 208  df-an 397  df-tru 1533  df-fal 1543  df-ex 1774  df-eu 2651
This theorem is referenced by:  unqsym1  33660
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