Theorem falnanfal 1357

Description: A -/\ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
falnanfal	|- (( F. -/\ F. ) <-> T. )

Proof of Theorem falnanfal

Step	Hyp	Ref	Expression
1		nannot 1293	. 2 |- (-. F. <-> ( F. -/\ F. ))
2		notfal 1349	. 2 |- (-. F. <-> T. )
3	1, 2	bitr3i 242	1 |- (( F. -/\ F. ) <-> T. )

This proof depends on syntax axioms:  -. wn 3   <-> wb 176   -/\ wnan 1287   T. wtru 1316   F. wfal 1317

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360  df-nan 1288  df-tru 1319  df-fal 1320

This theorem is used by: (None)