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Theorem unnt 32532
Description: There does not exist exactly one set, such that is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
unnt ¬ ∃!𝑥

Proof of Theorem unnt
StepHypRef Expression
1 nextnt 32529 . 2 ¬ ∃𝑥 ¬ ⊤
2 eunex 4889 . 2 (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
31, 2mto 188 1 ¬ ∃!𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wtru 1524  wex 1744  ∃!weu 2498
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-nul 4822  ax-pow 4873
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1526  df-ex 1745  df-nf 1750  df-eu 2502  df-mo 2503
This theorem is referenced by:  mont  32533
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