Theorem bifal 1383

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 1377	. 2 |- -. F.
3	1, 2	2false 350	1 |- ( ph <-> F. )

Syntax hints:   -. wn 3   <-> wb 184   F. wfal 1375

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 1373  df-fal 1376

This theorem is referenced by:  falantru  1396  trubifal  1409  bicontr  29020  aibnbaif  30061  ralnralall  30258  rusgra0edg  30713  frgrareg  30850  frgraregord013  30851  bj-df-nul  32821