Theorem falim 1587

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 1580. (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 1584	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 120	1 ⊢ (⊥ → 𝜑)

This proof depends on syntax axioms:   → wi 4  ⊥wfal 1582

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1573  df-fal 1583

This theorem is used by:  falimd  1588  tbw-bijust  1731  tbw-negdf  1732  tbw-ax4  1736  merco1  1746  merco2  1769  csbprc  4367  ralnralall  4469  tgcgr4  28987  frgrregord013  30989  nalfal  37171  imsym1  37186  consym1  37188  dissym1  37189  unisym1  37191  exisym1  37192  subsym1  37195  bj-falor2  37435  bj-cbvaw  37520  bj-cbveaw  37522  bj-prmoore  38016  wl-2mintru2  38394  orfa1  38999  orfa2  39000  bifald  39001  botel  39016  quadfac  43235  quantgodelALT  47854  lindslinindsimp2  49544