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Theorem nmotru 36391
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 1973 . . 3 𝑥
2 neutru 36390 . . 3 ¬ ∃!𝑥
3 jcn 162 . . 3 (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤)))
41, 2, 3mp2 9 . 2 ¬ (∃𝑥⊤ → ∃!𝑥⊤)
5 moeu 2581 . 2 (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤))
64, 5mtbir 323 1 ¬ ∃*𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wtru 1538  wex 1776  ∃*wmo 2536  ∃!weu 2566
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-10 2139  ax-12 2175  ax-nul 5312  ax-pow 5371
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-nf 1781  df-mo 2538  df-eu 2567
This theorem is referenced by: (None)
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