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Theorem unnt 31118
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 31115 . 2  |-  -.  E. x  -. T.
2 eunex 4613 . 2  |-  ( E! x T.  ->  E. x  -. T.  )
31, 2mto 181 1  |-  -.  E! x T.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   T. wtru 1456   E.wex 1674   E!weu 2310
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-8 1900  ax-9 1907  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-nul 4550  ax-pow 4598
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679  df-eu 2314  df-mo 2315
This theorem is referenced by:  mont  31119
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