Theorem trunantru 1354

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

Assertion

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

Proof of Theorem trunantru

Step	Hyp	Ref	Expression
1		nannot 1293	. 2 |- (-. T. <-> ( T. -/\ T. ))
2		nottru 1348	. 2 |- (-. T. <-> F. )
3	1, 2	bitr3i 242	1 |- (( T. -/\ T. ) <-> F. )

Syntax hints:  -. wn 3   <-> wb 176   -/\ 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-fal 1320

This theorem is referenced by: (None)