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Theorem unnt 25865
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 25862 . 2  |-  -.  E. x  -.  T.
2 eunex 4326 . 2  |-  ( E! x  T.  ->  E. x  -.  T.  )
31, 2mto 169 1  |-  -.  E! x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    T. wtru 1322   E.wex 1547   E!weu 2231
This theorem is referenced by:  mont  25866
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 1661  ax-8 1682  ax-13 1719  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-nul 4272  ax-pow 4311
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2235
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