Theorem bifal 1450

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 1444	. 2 |- -. F.
3	1, 2	2false 351	1 |- ( ph <-> F. )

Syntax hints:   -. wn 3   <-> wb 187   F. wfal 1442

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 188  df-tru 1440  df-fal 1443

This theorem is referenced by:  falantru  1461  trubifalOLD  1476  tgcgr4  24574  rusgra0edg  25681  frgrareg  25843  frgraregord013  25844  bj-df-nul  31588  bicontr  32277  aibnbaif  38365  aifftbifffaibif  38380  atnaiana  38382  ralnralall  38853