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  4330  csbprc  4360  ralf0  4465  ralnralall  4466  tgcgr4  28476  frgrregord013  30339  nalfal  36377  imsym1  36392  consym1  36394  dissym1  36395  unisym1  36397  exisym1  36398  subsym1  36401  bj-falor2  36559  bj-prmoore  37089  wl-2mintru2  37465  orfa1  38065  orfa2  38066  bifald  38067  botel  38084  lindslinindsimp2  48448