Users' Mathboxes Mathbox for Anthony Hart < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  nalf Unicode version

Theorem nalf 24842
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 24841 . 2  |-  A. x  -.  F.
2 falim 1319 . . 3  |-  (  F. 
->  -.  A. x  -.  F.  )
32sps 1739 . 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 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-tru 1310  df-fal 1311
  Copyright terms: Public domain W3C validator