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

Theorem mont 26071
Description: There does not exist at most one set, such that  T. is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
mont  |-  -.  E* x  T.

Proof of Theorem mont
StepHypRef Expression
1 extt 26066 . . 3  |-  E. x  T.
2 unnt 26070 . . 3  |-  -.  E! x  T.
3 mth8 140 . . 3  |-  ( E. x  T.  ->  ( -.  E! x  T.  ->  -.  ( E. x  T. 
->  E! x  T.  )
) )
41, 2, 3mp2 9 . 2  |-  -.  ( E. x  T.  ->  E! x  T.  )
5 df-mo 2267 . 2  |-  ( E* x  T.  <->  ( E. x  T.  ->  E! x  T.  ) )
64, 5mtbir 291 1  |-  -.  E* x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    T. wtru 1322   E.wex 1547   E!weu 2262   E*wmo 2263
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-13 1723  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-nul 4306  ax-pow 4345
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267
  Copyright terms: Public domain W3C validator