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Theorem falim 1256
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 1249 . 2 ¬ ⊥
21pm2.21i 574 1 ( ⊥ → φ)
Colors of variables: wff set class
Syntax hints:  wi 4  wfal 1247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248
This theorem is referenced by:  falimd  1257  falantru  1291  falimtru  1299  csbprc  3256
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