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Theorem unnt 26150
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 26147 . 2  |-  -.  E. x  -.  T.
2 eunex 4384 . 2  |-  ( E! x  T.  ->  E. x  -.  T.  )
31, 2mto 169 1  |-  -.  E! x  T.
Colors of variables: wff set class
Syntax hints:   -. wn 3    T. wtru 1325   E.wex 1550   E!weu 2280
This theorem is referenced by:  mont  26151
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-nul 4330  ax-pow 4369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284
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