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Theorem falim 1451
Description: The truth value F. implies anything. Also called the "principle of explosion", or "ex falso [sequitur]] quodlibet" (Latin for "from falsehood, anything [follows]]"). (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)
Assertion
Ref Expression
falim  |-  ( F. 
->  ph )

Proof of Theorem falim
StepHypRef Expression
1 fal 1444 . 2  |-  -. F.
21pm2.21i 134 1  |-  ( F. 
->  ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   F. wfal 1442
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 188  df-tru 1440  df-fal 1443
This theorem is referenced by:  falimd  1452  dfnotOLD  1457  falimtru  1471  tbw-bijust  1577  tbw-negdf  1578  tbw-ax4  1582  merco1  1592  merco2  1615  csbprc  3798  tgcgr4  24563  frgrareg  25831  frgraregord013  25832  nalf  31056  imsym1  31071  consym1  31073  dissym1  31074  unisym1  31076  exisym1  31077  bj-falor2  31161  orfa1  32234  orfa2  32235  bifald  32236  botel  32255  ralnralall  38693  lindslinindsimp2  39530
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