Theorem falim 1558

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 1551. (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 1555	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 119	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1553

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 1544  df-fal 1554

This theorem is referenced by:  falimd  1559  tbw-bijust  1699  tbw-negdf  1700  tbw-ax4  1704  merco1  1714  merco2  1737  csbprc  4359  ralnralall  4464  tgcgr4  28552  frgrregord013  30419  nalfal  36546  imsym1  36561  consym1  36563  dissym1  36564  unisym1  36566  exisym1  36567  subsym1  36570  bj-falor2  36728  bj-prmoore  37259  wl-2mintru2  37635  orfa1  38225  orfa2  38226  bifald  38227  botel  38244  lindslinindsimp2  48651