MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  falim Structured version   Visualization version   GIF version

Theorem falim 1495
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 1487 . 2 ¬ ⊥
21pm2.21i 116 1 (⊥ → 𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wfal 1485
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 1483  df-fal 1486
This theorem is referenced by:  falimd  1496  falimtru  1513  tbw-bijust  1620  tbw-negdf  1621  tbw-ax4  1625  merco1  1635  merco2  1658  csbprc  3958  csbprcOLD  3959  ralnralall  4058  tgcgr4  25360  frgrregord013  27141  nalf  32097  imsym1  32112  consym1  32114  dissym1  32115  unisym1  32117  exisym1  32118  bj-falor2  32265  orfa1  33557  orfa2  33558  bifald  33559  botel  33577  lindslinindsimp2  41570
  Copyright terms: Public domain W3C validator