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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  2427  rabxm  3452  elimif  3568  ixxun  10638  lgsquadlem2  20556  fvresval  23492  condis  24308  condisd  24309  altdftru  24314  pdiveql  25535  uunT1  27605  onfrALTVD  27717  a9e2ndeqVD  27735  a9e2ndeqALT  27758  bnj1304  27901  a12study4  28284
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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