Theorem truxortru 1419

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 1376	. 2 |- ( ( T. \/_ T. ) <-> ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) )
2		oridm 757	. . 3 |- ( ( T. \/ T. ) <-> T. )
3		nottru 1413	. . . 4 |- ( -. T. <-> F. )
4		anidm 396	. . . 4 |- ( ( T. /\ T. ) <-> T. )
5	3, 4	xchnxbir 681	. . 3 |- ( -. ( T. /\ T. ) <-> F. )
6	2, 5	anbi12i 460	. 2 |- ( ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) <-> ( T. /\ F. ) )
7		truan 1370	. 2 |- ( ( T. /\ F. ) <-> F. )
8	1, 6, 7	3bitri 206	1 |- ( ( T. \/_ T. ) <-> F. )

Syntax hints:   -. wn 3   /\ wa 104   <-> wb 105   \/ wo 708   T. wtru 1354   F. wfal 1358   \/_ wxo 1375

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359  df-xor 1376

This theorem is referenced by: (None)