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

Theorem unnt 24847
Description: There does not exist exactly one set, such that  T. is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
unnt  |-  -.  E! x  T.

Proof of Theorem unnt
StepHypRef Expression
1 nextnt 24844 . 2  |-  -.  E. x  -.  T.
2 eunex 4203 . 2  |-  ( E! x  T.  ->  E. x  -.  T.  )
31, 2mto 167 1  |-  -.  E! x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    T. wtru 1307   E.wex 1528   E!weu 2143
This theorem is referenced by:  mont  24848
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-13 1686  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-nul 4149  ax-pow 4188
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147
  Copyright terms: Public domain W3C validator