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Theorem nalf 26155
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 26154 . 2  |-  A. x  -.  F.
2 falim 1338 . . 3  |-  (  F. 
->  -.  A. x  -.  F.  )
32sps 1771 . 2  |-  ( A. x  F.  ->  -.  A. x  -.  F.  )
41, 3mt2 173 1  |-  -.  A. x  F.
Colors of variables: wff set class
Syntax hints:   -. wn 3    F. wfal 1327   A.wal 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-tru 1329  df-fal 1330  df-ex 1552
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