Theorem nbfal 1495

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 1490	. 2 |- -. F.
2	1	nbn 362	1 |- ( -. ph <-> ( ph <-> F. ) )

Syntax hints:   -. wn 3   <-> wb 196   F. wfal 1488

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 197  df-tru 1486  df-fal 1489

This theorem is referenced by:  zfnuleu  4786  bisym1  32418  aisfina  41065  aifftbifffaibifff  41089  lindslinindsimp2  42252