Theorem falxortru 1312

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

Assertion

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

Proof of Theorem falxortru

Step	Hyp	Ref	Expression
1		df-xor 1267	. 2 |- ( ( F. \/_ T. ) <-> ( ( F. \/ T. ) /\ -. ( F. /\ T. ) ) )
2		falortru 1298	. . 3 |- ( ( F. \/ T. ) <-> T. )
3		notfal 1305	. . . 4 |- ( -. F. <-> T. )
4		falantru 1294	. . . 4 |- ( ( F. /\ T. ) <-> F. )
5	3, 4	xchnxbir 606	. . 3 |- ( -. ( F. /\ T. ) <-> T. )
6	2, 5	anbi12i 433	. 2 |- ( ( ( F. \/ T. ) /\ -. ( F. /\ T. ) ) <-> ( T. /\ T. ) )
7		anidm 376	. 2 |- ( ( T. /\ T. ) <-> T. )
8	1, 6, 7	3bitri 195	1 |- ( ( F. \/_ T. ) <-> T. )

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)