Theorem nbfal 1375

Description: The negation of a proposition is equivalent to itself being equivalent to F.. (Contributed by Anthony Hart, 14-Aug-2011.)

Assertion

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

Proof of Theorem nbfal

Step	Hyp	Ref	Expression
1		fal 1371	. 2 |- -. F.
2	1	nbn 700	1 |- ( -. ph <-> ( ph <-> F. ) )

Syntax hints:   -. wn 3   <-> wb 105   F. wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  zfnuleu  4158