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Theorem falim 1538
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 1530 . 2 ¬ ⊥
21pm2.21i 116 1 (⊥ → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1528
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 197  df-tru 1526  df-fal 1529
This theorem is referenced by:  falimd  1539  falimtru  1556  tbw-bijust  1663  tbw-negdf  1664  tbw-ax4  1668  merco1  1678  merco2  1701  csbprc  4013  csbprcOLD  4014  ralnralall  4113  tgcgr4  25471  frgrregord013  27382  nalf  32527  imsym1  32542  consym1  32544  dissym1  32545  unisym1  32547  exisym1  32548  bj-falor2  32695  orfa1  34016  orfa2  34017  bifald  34018  botel  34036  lindslinindsimp2  42577
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