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Theorem mont 29727
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 29722 . . 3  |-  E. x T.
2 unnt 29726 . . 3  |-  -.  E! x T.
3 mth8 146 . . 3  |-  ( E. x T.  ->  ( -.  E! x T.  ->  -.  ( E. x T. 
->  E! x T.  ) ) )
41, 2, 3mp2 9 . 2  |-  -.  ( E. x T.  ->  E! x T.  )
5 df-mo 2280 . 2  |-  ( E* x T.  <->  ( E. x T.  ->  E! x T.  ) )
64, 5mtbir 299 1  |-  -.  E* x T.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   T. wtru 1380   E.wex 1596   E!weu 2275   E*wmo 2276
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-nul 4576  ax-pow 4625
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-eu 2279  df-mo 2280
This theorem is referenced by: (None)
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