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Theorem mont 25675
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 25670 . . 3  |-  E. x  T.
2 unnt 25674 . . 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 2222 . 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 1321   E.wex 1546   E!weu 2217   E*wmo 2218
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-13 1717  ax-14 1719  ax-6 1734  ax-7 1739  ax-11 1751  ax-12 1937  ax-nul 4251  ax-pow 4290
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1324  df-ex 1547  df-nf 1550  df-sb 1654  df-eu 2221  df-mo 2222
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