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Theorem falim 1273
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 1266 . 2 ¬ ⊥
21pm2.21i 585 1 (⊥ → 𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wfal 1264
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265
This theorem is referenced by:  falimd  1274  falantru  1310  falimtru  1318  csbprc  3289
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