Theorem falim 1378

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 1371	. 2 ⊢ ¬ ⊥
2	1	pm2.21i 647	1 ⊢ (⊥ → 𝜑)

Syntax hints:   → wi 4  ⊥wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  falimd  1379  falantru  1414  falimtru  1422  csbprc  3496