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Theorem unnf 32531
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 32530 . 2 ¬ ∃𝑥
2 euex 2522 . 2 (∃!𝑥⊥ → ∃𝑥⊥)
31, 2mto 188 1 ¬ ∃!𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wfal 1528  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
This theorem depends on definitions:  df-bi 197  df-tru 1526  df-fal 1529  df-ex 1745  df-eu 2502
This theorem is referenced by:  unqsym1  32549
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