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Theorem mont 24848
Description: There does not exist at most one set, such that  T. is true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
mont  |-  -.  E* x  T.

Proof of Theorem mont
StepHypRef Expression
1 extt 24843 . . 3  |-  E. x  T.
2 unnt 24847 . . 3  |-  -.  E! x  T.
3 mth8 138 . . 3  |-  ( E. x  T.  ->  ( -.  E! x  T.  ->  -.  ( E. x  T. 
->  E! x  T.  )
) )
41, 2, 3mp2 17 . 2  |-  -.  ( E. x  T.  ->  E! x  T.  )
5 df-mo 2148 . 2  |-  ( E* x  T.  <->  ( E. x  T.  ->  E! x  T.  ) )
64, 5mtbir 290 1  |-  -.  E* x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    T. wtru 1307   E.wex 1528   E!weu 2143   E*wmo 2144
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-fal 1311  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148
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