Theorem falim 1564

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 1557. (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 1561	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1559

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 208  df-tru 1550  df-fal 1560

This theorem is referenced by:  falimd  1565  tbw-bijust  1705  tbw-negdf  1706  tbw-ax4  1710  merco1  1720  merco2  1743  csbprc  4337  ralnralall  4441  tgcgr4  28617  frgrregord013  30483  nalfal  36631  imsym1  36646  consym1  36648  dissym1  36649  unisym1  36651  exisym1  36652  subsym1  36655  bj-falor2  36896  bj-cbvaw  36981  bj-cbveaw  36983  bj-prmoore  37473  wl-2mintru2  37853  orfa1  38452  orfa2  38453  bifald  38454  botel  38471  quantgodelALT  47318  lindslinindsimp2  48954