Theorem truxortru 1310

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 1267	. 2 |- ( ( T. \/_ T. ) <-> ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) )
2		oridm 674	. . 3 |- ( ( T. \/ T. ) <-> T. )
3		nottru 1304	. . . 4 |- ( -. T. <-> F. )
4		anidm 376	. . . 4 |- ( ( T. /\ T. ) <-> T. )
5	3, 4	xchnxbir 606	. . 3 |- ( -. ( T. /\ T. ) <-> F. )
6	2, 5	anbi12i 433	. 2 |- ( ( ( T. \/ T. ) /\ -. ( T. /\ T. ) ) <-> ( T. /\ F. ) )
7		truan 1260	. 2 |- ( ( T. /\ F. ) <-> F. )
8	1, 6, 7	3bitri 195	1 |- ( ( T. \/_ T. ) <-> F. )

Syntax hints:   -. wn 3   /\ wa 97   <-> wb 98   \/ wo 629   T. wtru 1244   F. wfal 1248   \/_ wxo 1266

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-xor 1267

This theorem is referenced by: (None)