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Theorem nmotru 33774
 Description: There does not exist at most one set such that ⊤ is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
nmotru ¬ ∃*𝑥

Proof of Theorem nmotru
StepHypRef Expression
1 extru 1981 . . 3 𝑥
2 neutru 33773 . . 3 ¬ ∃!𝑥
3 jcn 165 . . 3 (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤)))
41, 2, 3mp2 9 . 2 ¬ (∃𝑥⊤ → ∃!𝑥⊤)
5 moeu 2669 . 2 (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤))
64, 5mtbir 326 1 ¬ ∃*𝑥
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ⊤wtru 1539  ∃wex 1781  ∃*wmo 2622  ∃!weu 2654 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-12 2179  ax-nul 5191  ax-pow 5247 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-mo 2624  df-eu 2655 This theorem is referenced by: (None)
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