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Theorem falim 1489
 Description: The truth value ⊥ 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 (⊥ → 𝜑)

Proof of Theorem falim
StepHypRef Expression
1 fal 1482 . 2 ¬ ⊥
21pm2.21i 115 1 (⊥ → 𝜑)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ⊥wfal 1480 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 196  df-tru 1478  df-fal 1481 This theorem is referenced by:  falimd  1490  falimtru  1507  tbw-bijust  1614  tbw-negdf  1615  tbw-ax4  1619  merco1  1629  merco2  1652  csbprc  3932  csbprcOLD  3933  tgcgr4  25226  frgrareg  26644  frgraregord013  26645  nalf  31572  imsym1  31587  consym1  31589  dissym1  31590  unisym1  31592  exisym1  31593  bj-falor2  31743  orfa1  33056  orfa2  33057  bifald  33058  botel  33076  ralnralall  40307  av-frgraregord013  41549  lindslinindsimp2  42046
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