Theorem falim 1557

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 1550. (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 1554	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1552

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 1543  df-fal 1553

This theorem is referenced by:  falimd  1558  tbw-bijust  1698  tbw-negdf  1699  tbw-ax4  1703  merco1  1713  merco2  1736  ab0w  4354  csbprc  4384  ralf0  4489  ralnralall  4490  tgcgr4  28456  frgrregord013  30322  nalfal  36367  imsym1  36382  consym1  36384  dissym1  36385  unisym1  36387  exisym1  36388  subsym1  36391  bj-falor2  36549  bj-prmoore  37079  wl-2mintru2  37455  orfa1  38055  orfa2  38056  bifald  38057  botel  38074  lindslinindsimp2  48387