Theorem bifal 1297

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 1291	. 2 |- -. F.
3	1, 2	2false 649	1 |- ( ph <-> F. )

Syntax hints:   -. wn 3   <-> wb 103   F. wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by: (None)