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

Theorem mont 26164
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 26159 . . 3  |-  E. x  T.
2 unnt 26163 . . 3  |-  -.  E! x  T.
3 mth8 141 . . 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 2288 . 2  |-  ( E* x  T.  <->  ( E. x  T.  ->  E! x  T.  ) )
64, 5mtbir 292 1  |-  -.  E* x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    T. wtru 1326   E.wex 1551   E!weu 2283   E*wmo 2284
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-13 1728  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-nul 4341  ax-pow 4380
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288
  Copyright terms: Public domain W3C validator