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Theorem mont 31578
 Description: There does not exist at most one set, such that ⊤ is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
mont ¬ ∃*𝑥

Proof of Theorem mont
StepHypRef Expression
1 extt 31573 . . 3 𝑥
2 unnt 31577 . . 3 ¬ ∃!𝑥
3 mth8 157 . . 3 (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤)))
41, 2, 3mp2 9 . 2 ¬ (∃𝑥⊤ → ∃!𝑥⊤)
5 df-mo 2463 . 2 (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤))
64, 5mtbir 312 1 ¬ ∃*𝑥
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ⊤wtru 1476  ∃wex 1695  ∃!weu 2458  ∃*wmo 2459 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-nul 4717  ax-pow 4769 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-eu 2462  df-mo 2463 This theorem is referenced by: (None)
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