Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  mont Structured version   Visualization version   GIF version

Theorem mont 32725
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 32720 . . 3 𝑥
2 unnt 32724 . . 3 ¬ ∃!𝑥
3 mth8 159 . . 3 (∃𝑥⊤ → (¬ ∃!𝑥⊤ → ¬ (∃𝑥⊤ → ∃!𝑥⊤)))
41, 2, 3mp2 9 . 2 ¬ (∃𝑥⊤ → ∃!𝑥⊤)
5 df-mo 2635 . 2 (∃*𝑥⊤ ↔ (∃𝑥⊤ → ∃!𝑥⊤))
64, 5mtbir 314 1 ¬ ∃*𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wtru 1638  wex 1859  ∃!weu 2630  ∃*wmo 2631
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1877  ax-4 1894  ax-5 2001  ax-6 2068  ax-7 2104  ax-8 2158  ax-9 2165  ax-10 2185  ax-11 2201  ax-12 2214  ax-13 2420  ax-nul 4983  ax-pow 5035
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 866  df-tru 1641  df-ex 1860  df-nf 1864  df-eu 2634  df-mo 2635
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator