Theorem bifal 1412

Description: A contradiction is equivalent to falsehood. (Contributed by Mario Carneiro, 9-May-2015.)

Hypothesis

Ref	Expression
bifal.1	|- -. ph

Assertion

Ref	Expression
bifal	|- ( ph <-> F. )

Proof of Theorem bifal

Step	Hyp	Ref	Expression
1		bifal.1	. 2 |- -. ph
2		fal 1406	. 2 |- -. F.
3	1, 2	2false 348	1 |- ( ph <-> F. )

Syntax hints:   -. wn 3   <-> wb 184   F. wfal 1404

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-tru 1402  df-fal 1405

This theorem is referenced by:  falantru  1425  trubifalOLD  1440  rusgra0edg  25076  frgrareg  25238  frgraregord013  25239  bicontr  30643  aibnbaif  32268  ralnralall  32615  bj-df-nul  34932