Theorem falim 1587

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 1580. (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 1584	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 120	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1582

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 210  df-tru 1573  df-fal 1583

This theorem is referenced by:  falimd  1588  tbw-bijust  1728  tbw-negdf  1729  tbw-ax4  1733  merco1  1743  merco2  1766  csbprc  4374  ralnralall  4474  tgcgr4  28800  frgrregord013  30746  nalfal  36914  imsym1  36929  consym1  36931  dissym1  36932  unisym1  36934  exisym1  36935  subsym1  36938  bj-falor2  37178  bj-cbvaw  37263  bj-cbveaw  37265  bj-prmoore  37757  wl-2mintru2  38137  orfa1  38736  orfa2  38737  bifald  38738  botel  38753  quadfac  42972  quantgodelALT  47589  lindslinindsimp2  49243