Theorem trunanfal 1355

Description: A -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

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

Proof of Theorem trunanfal

Step	Hyp	Ref	Expression
1		df-nan 1288	. 2 |- (( T. -/\ F. ) <-> -. ( T. /\ F. ))
2		truanfal 1337	. . 3 |- (( T. /\ F. ) <-> F. )
3	2	notbii 287	. 2 |- (-. ( T. /\ F. ) <-> -. F. )
4		notfal 1349	. 2 |- (-. F. <-> T. )
5	1, 3, 4	3bitri 262	1 |- (( T. -/\ F. ) <-> T. )

Syntax hints:  -. wn 3   <-> wb 176   /\ wa 358   -/\ wnan 1287   T. wtru 1316   F. wfal 1317

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 177  df-an 360  df-nan 1288  df-tru 1319  df-fal 1320

This theorem is referenced by:  falnantru  1356