Theorem truxorfal 1529

Description: A \/_ identity. (Contributed by David A. Wheeler, 8-May-2015.)

Assertion

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

Proof of Theorem truxorfal

Step	Hyp	Ref	Expression
1		df-xor 1465	. . 3 |- ( ( T. \/_ F. ) <-> -. ( T. <-> F. ) )
2		trubifal 1522	. . 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   \/_ wxo 1464   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-xor 1465  df-tru 1486  df-fal 1489

This theorem is referenced by:  falxortru  1530