Theorem falim 1584

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 1577. (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 1581	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 120	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1579

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 1570  df-fal 1580

This theorem is referenced by:  falimd  1585  tbw-bijust  1725  tbw-negdf  1726  tbw-ax4  1730  merco1  1740  merco2  1763  csbprc  4380  ralnralall  4479  tgcgr4  28765  frgrregord013  30686  nalfal  36802  imsym1  36817  consym1  36819  dissym1  36820  unisym1  36822  exisym1  36823  subsym1  36826  bj-falor2  37066  bj-cbvaw  37151  bj-cbveaw  37153  bj-prmoore  37644  wl-2mintru2  38024  orfa1  38623  orfa2  38624  bifald  38625  botel  38642  quadfac  42861  quantgodelALT  47480  lindslinindsimp2  49127