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  4344  csbprc  4374  ralf0  4479  ralnralall  4480  tgcgr4  28464  frgrregord013  30330  nalfal  36386  imsym1  36401  consym1  36403  dissym1  36404  unisym1  36406  exisym1  36407  subsym1  36410  bj-falor2  36568  bj-prmoore  37098  wl-2mintru2  37474  orfa1  38074  orfa2  38075  bifald  38076  botel  38093  lindslinindsimp2  48442