Theorem falim 1498

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 1490	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 116	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1488

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 1486  df-fal 1489

This theorem is referenced by:  falimd  1499  falimtru  1516  tbw-bijust  1623  tbw-negdf  1624  tbw-ax4  1628  merco1  1638  merco2  1661  csbprc  3980  csbprcOLD  3981  ralnralall  4080  tgcgr4  25426  frgrregord013  27253  nalf  32402  imsym1  32417  consym1  32419  dissym1  32420  unisym1  32422  exisym1  32423  bj-falor2  32570  orfa1  33886  orfa2  33887  bifald  33888  botel  33906  lindslinindsimp2  42252