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Theorem unnt 32634
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 32631 . 2 ¬ ∃𝑥 ¬ ⊤
2 eunex 4964 . 2 (∃!𝑥⊤ → ∃𝑥 ¬ ⊤)
31, 2mto 188 1 ¬ ∃!𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wtru 1597  wex 1817  ∃!weu 2571
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-8 2105  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-nul 4897  ax-pow 4948
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-eu 2575  df-mo 2576
This theorem is referenced by:  mont  32635
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