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Theorem nalf 31062
Description: Not all sets hold F. as true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
nalf  |-  -.  A. x F.

Proof of Theorem nalf
StepHypRef Expression
1 alnof 31061 . 2  |-  A. x  -. F.
2 falim 1452 . . 3  |-  ( F. 
->  -.  A. x  -. F.  )
32sps 1917 . 2  |-  ( A. x F.  ->  -.  A. x  -. F.  )
41, 3mt2 183 1  |-  -.  A. x F.
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   A.wal 1436   F. wfal 1443
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-12 1906
This theorem depends on definitions:  df-bi 189  df-tru 1441  df-fal 1444  df-ex 1661
This theorem is referenced by: (None)
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