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Theorem nmotru 35794
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 1971 . . 3 𝑥
2 neutru 35793 . . 3 ¬ ∃!𝑥
3 jcn 162 . . 3 (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤)))
41, 2, 3mp2 9 . 2 ¬ (∃𝑥⊤ → ∃!𝑥⊤)
5 moeu 2569 . 2 (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤))
64, 5mtbir 323 1 ¬ ∃*𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wtru 1534  wex 1773  ∃*wmo 2524  ∃!weu 2554
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-12 2163  ax-nul 5297  ax-pow 5354
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-mo 2526  df-eu 2555
This theorem is referenced by: (None)
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