Theorem truxortru 1409

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

Assertion

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

Proof of Theorem truxortru

Step	Hyp	Ref	Expression
1		df-xor 1366	. 2 |- ( ( T. \/_ T. ) <-> ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) )
2		oridm 747	. . 3 |- ( ( T. \/ T. ) <-> T. )
3		nottru 1403	. . . 4 |- ( -. T. <-> F. )
4		anidm 394	. . . 4 |- ( ( T. /\ T. ) <-> T. )
5	3, 4	xchnxbir 671	. . 3 |- ( -. ( T. /\ T. ) <-> F. )
6	2, 5	anbi12i 456	. 2 |- ( ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) <-> ( T. /\ F. ) )
7		truan 1360	. 2 |- ( ( T. /\ F. ) <-> F. )
8	1, 6, 7	3bitri 205	1 |- ( ( T. \/_ T. ) <-> F. )

Syntax hints:   -. wn 3   /\ wa 103   <-> wb 104   \/ wo 698   T. wtru 1344   F. wfal 1348   \/_ wxo 1365

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-fal 1349  df-xor 1366

This theorem is referenced by: (None)