Theorem falxortru 1360

Description: A \/_ identity. (Contributed by David A. Wheeler, 9-May-2015.)

Assertion

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

Proof of Theorem falxortru

Step	Hyp	Ref	Expression
1		df-xor 1305	. 2 |- (( F. \/_ T. ) <-> -. ( F. <-> T. ))
2		falbitru 1352	. . 3 |- (( F. <-> T. ) <-> F. )
3	2	notbii 287	. 2 |- (-. ( F. <-> T. ) <-> -. F. )
4		notfal 1349	. 2 |- (-. F. <-> T. )
5	1, 3, 4	3bitri 262	1 |- (( F. \/_ T. ) <-> 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)