Theorem falim 1559

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 1552. (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 1556	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1554

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 1545  df-fal 1555

This theorem is referenced by:  falimd  1560  tbw-bijust  1700  tbw-negdf  1701  tbw-ax4  1705  merco1  1715  merco2  1738  csbprc  4363  ralnralall  4468  tgcgr4  28615  frgrregord013  30482  nalfal  36619  imsym1  36634  consym1  36636  dissym1  36637  unisym1  36639  exisym1  36640  subsym1  36643  bj-falor2  36810  bj-cbvaw  36884  bj-cbveaw  36886  bj-prmoore  37368  wl-2mintru2  37746  orfa1  38336  orfa2  38337  bifald  38338  botel  38355  lindslinindsimp2  48823