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Theorem unnt 24919
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 24916 . 2  |-  -.  E. x  -.  T.
2 eunex 4219 . 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 1531   E!weu 2156
This theorem is referenced by:  mont  24920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-nul 4165  ax-pow 4204
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160
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