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Theorem falim 1328
Description: The truth value implies anything. Also called the principle of explosion, or "ex falso quodlibet". (Contributed by FL, 20-Mar-2011.) (Proof shortened by Anthony Hart, 1-Aug-2011.)
Assertion
Ref Expression
falim (⊥ → 𝜑)

Proof of Theorem falim
StepHypRef Expression
1 fal 1321 . 2 ¬ ⊥
21pm2.21i 618 1 (⊥ → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wfal 1319
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320
This theorem is referenced by:  falimd  1329  falantru  1364  falimtru  1372  csbprc  3376
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