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Theorem unnt 30894
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 30891 . 2  |-  -.  E. x  -. T.
2 eunex 4609 . 2  |-  ( E! x T.  ->  E. x  -. T.  )
31, 2mto 179 1  |-  -.  E! x T.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   T. wtru 1438   E.wex 1659   E!weu 2263
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-8 1869  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-nul 4547  ax-pow 4594
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-eu 2267  df-mo 2268
This theorem is referenced by:  mont  30895
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