Theorem falim 1645

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

Step	Hyp	Ref	Expression
1		fal 1637	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 116	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1635

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 1633  df-fal 1636

This theorem is referenced by:  falimd  1646  falimtru  1663  tbw-bijust  1770  tbw-negdf  1771  tbw-ax4  1775  merco1  1785  merco2  1808  csbprc  4121  csbprcOLD  4122  ralnralall  4222  tgcgr4  25623  frgrregord013  27561  nalf  32706  imsym1  32721  consym1  32723  dissym1  32724  unisym1  32726  exisym1  32727  bj-falor2  32874  orfa1  34197  orfa2  34198  bifald  34199  botel  34217  lindslinindsimp2  42760