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Theorem exmid 406
Description: Law of excluded middle, also called the principle of tertium non datur. Theorem *2.11 of [WhiteheadRussell] p. 101. It says that something is either true or not true; there are no in-between values of truth. This is an essential distinction of our classical logic and is not a theorem of intuitionistic logic. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
exmid  |-  ( ph  \/  -.  ph )

Proof of Theorem exmid
StepHypRef Expression
1 id 21 . 2  |-  ( -. 
ph  ->  -.  ph )
21orri 367 1  |-  ( ph  \/  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 5    \/ wo 359
This theorem is referenced by:  exmidd  407  pm5.62  894  pm5.63  895  pm4.83  900  4exmid  910  exmidne  2418  rabxm  3384  elimif  3499  ixxun  10550  lgsquadlem2  20426  fvresval  23291  condis  24107  condisd  24108  altdftru  24113  pdiveql  25334  uunT1  27342  onfrALTVD  27454  a9e2ndeqVD  27472  a9e2ndeqALT  27495  bnj1304  27638  a12study4  28021
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361
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