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Theorem nalf 24914
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 24913 . 2  |-  A. x  -.  F.
2 falim 1319 . . 3  |-  (  F. 
->  -.  A. x  -.  F.  )
32sps 1751 . 2  |-  ( A. x  F.  ->  -.  A. x  -.  F.  )
41, 3mt2 170 1  |-  -.  A. x  F.
Colors of variables: wff set class
Syntax hints:   -. wn 3    F. wfal 1308   A.wal 1530
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-fal 1311
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