Theorem falim 1555

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 1548. (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 1552	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1550

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 1541  df-fal 1551

This theorem is referenced by:  falimd  1556  tbw-bijust  1700  tbw-negdf  1701  tbw-ax4  1705  merco1  1715  merco2  1738  csbprc  4313  ralnralall  4416  tgcgr4  26325  frgrregord013  28180  nalfal  33864  imsym1  33879  consym1  33881  dissym1  33882  unisym1  33884  exisym1  33885  bj-falor2  34032  bj-prmoore  34530  wl-2mintru2  34908  orfa1  35523  orfa2  35524  bifald  35525  botel  35542  lindslinindsimp2  44872