Theorem truxorfal 1351

Description: A \/_ identity. (Contributed by David A. Wheeler, 2-Mar-2018.)

Assertion

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

Proof of Theorem truxorfal

Step	Hyp	Ref	Expression
1		df-xor 1307	. 2 |- ( ( T. \/_ F. ) <-> ( ( T. \/ F. ) /\ -. ( T. /\ F. ) ) )
2		truorfal 1337	. . 3 |- ( ( T. \/ F. ) <-> T. )
3		notfal 1345	. . . 4 |- ( -. F. <-> T. )
4		truan 1301	. . . 4 |- ( ( T. /\ F. ) <-> F. )
5	3, 4	xchnxbir 638	. . 3 |- ( -. ( T. /\ F. ) <-> T. )
6	2, 5	anbi12i 447	. 2 |- ( ( ( T. \/ F. ) /\ -. ( T. /\ F. ) ) <-> ( T. /\ T. ) )
7		anidm 388	. 2 |- ( ( T. /\ T. ) <-> T. )
8	1, 6, 7	3bitri 204	1 |- ( ( T. \/_ F. ) <-> T. )

Syntax hints:   -. wn 3   /\ wa 102   <-> wb 103   \/ wo 661   T. wtru 1285   F. wfal 1289   \/_ wxo 1306

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-io 662

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290  df-xor 1307

This theorem is referenced by: (None)