Theorem trunanfal 1525

Description: A -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)

Assertion

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

Proof of Theorem trunanfal

Step	Hyp	Ref	Expression
1		df-nan 1448	. . 3 |- ( ( T. -/\ F. ) <-> -. ( T. /\ F. ) )
2		truanfal 1507	. . 3 |- ( ( T. /\ F. ) <-> F. )
3	1, 2	xchbinx 324	. 2 |- ( ( T. -/\ F. ) <-> -. F. )
4		notfal 1519	. 2 |- ( -. F. <-> T. )
5	3, 4	bitri 264	1 |- ( ( T. -/\ F. ) <-> T. )

Syntax hints:   -. wn 3   <-> wb 196   /\ wa 384   -/\ wnan 1447   T. wtru 1484   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-an 386  df-nan 1448  df-tru 1486  df-fal 1489

This theorem is referenced by:  falnantru  1526