Theorem falim 1558

Description: The truth value ⊥ implies anything. Also called the "principle of explosion", or "ex falso [sequitur]] quodlibet" (Latin for "from falsehood, anything [follows]]"). Dual statement of trud 1551. (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 1555	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1553

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 207  df-tru 1544  df-fal 1554

This theorem is referenced by:  falimd  1559  tbw-bijust  1699  tbw-negdf  1700  tbw-ax4  1704  merco1  1714  merco2  1737  csbprc  4361  ralnralall  4466  tgcgr4  28603  frgrregord013  30470  nalfal  36597  imsym1  36612  consym1  36614  dissym1  36615  unisym1  36617  exisym1  36618  subsym1  36621  bj-falor2  36785  bj-prmoore  37320  wl-2mintru2  37696  orfa1  38286  orfa2  38287  bifald  38288  botel  38305  lindslinindsimp2  48709