Theorem falim 1416

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 1409	. 2 |- -. F.
2	1	pm2.21i 655	1 |- ( F. -> ph )

This proof depends on syntax axioms:   -> wi 4   F. wfal 1407

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 623  ax-in2 624

This proof depends on definitions:  df-bi 117  df-tru 1405  df-fal 1408

This theorem is used by:  falimd  1417  falantru  1452  falimtru  1460  csbprc  3572