Theorem falim 1257

Description: The truth value F. 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	|- ( F. -> ph )

Proof of Theorem falim

Step	Hyp	Ref	Expression
1		fal 1250	. 2 |- -. F.
2	1	pm2.21i 575	1 |- ( F. -> ph )

Syntax hints:   -> wi 4   F. wfal 1248

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 1246  df-fal 1249

This theorem is referenced by:  falimd  1258  falantru  1294  falimtru  1302  csbprc  3262