Theorem falim 1298

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

Step	Hyp	Ref	Expression
1		fal 1291	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 607	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  falimd  1299  falantru  1334  falimtru  1342  csbprc  3289