Theorem truxorfal 1359

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 1305	. . 3 |- (( T. \/_ F. ) <-> -. ( T. <-> F. ))
2		trubifal 1351	. . 3 |- (( T. <-> F. ) <-> F. )
3	1, 2	xchbinx 301	. 2 |- (( T. \/_ F. ) <-> -. F. )
4		notfal 1349	. 2 |- (-. F. <-> T. )
5	3, 4	bitri 240	1 |- (( T. \/_ F. ) <-> T. )

Syntax hints:  -. wn 3   <-> wb 176   \/_ wxo 1304   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-xor 1305  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)