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Theorem falim 1488
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 1481 . 2 ¬ ⊥
21pm2.21i 114 1 (⊥ → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1479
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 195  df-tru 1477  df-fal 1480
This theorem is referenced by:  falimd  1489  falimtru  1506  tbw-bijust  1613  tbw-negdf  1614  tbw-ax4  1618  merco1  1628  merco2  1651  csbprc  3931  csbprcOLD  3932  tgcgr4  25171  frgrareg  26437  frgraregord013  26438  nalf  31365  imsym1  31380  consym1  31382  dissym1  31383  unisym1  31385  exisym1  31386  bj-falor2  31536  orfa1  32839  orfa2  32840  bifald  32841  botel  32859  ralnralall  40091  av-frgraregord013  41530  lindslinindsimp2  42027
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