Theorem falxorfal 1354

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

Assertion

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

Proof of Theorem falxorfal

Step	Hyp	Ref	Expression
1		df-xor 1308	. 2 |- ( ( F. \/_ F. ) <-> ( ( F. \/ F. ) /\ -. ( F. /\ F. ) ) )
2		oridm 707	. . 3 |- ( ( F. \/ F. ) <-> F. )
3		notfal 1346	. . . 4 |- ( -. F. <-> T. )
4		anidm 388	. . . 4 |- ( ( F. /\ F. ) <-> F. )
5	3, 4	xchnxbir 639	. . 3 |- ( -. ( F. /\ F. ) <-> T. )
6	2, 5	anbi12i 448	. 2 |- ( ( ( F. \/ F. ) /\ -. ( F. /\ F. ) ) <-> ( F. /\ T. ) )
7		falantru 1335	. 2 |- ( ( F. /\ T. ) <-> F. )
8	1, 6, 7	3bitri 204	1 |- ( ( F. \/_ F. ) <-> F. )

Syntax hints:   -. wn 3   /\ wa 102   <-> wb 103   \/ wo 662   T. wtru 1286   F. wfal 1290   \/_ wxo 1307

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 577  ax-in2 578  ax-io 663

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-xor 1308

This theorem is referenced by: (None)