Theorem falxorfal 1417

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 1371	. 2 |- ( ( F. \/_ F. ) <-> ( ( F. \/ F. ) /\ -. ( F. /\ F. ) ) )
2		oridm 752	. . 3 |- ( ( F. \/ F. ) <-> F. )
3		notfal 1409	. . . 4 |- ( -. F. <-> T. )
4		anidm 394	. . . 4 |- ( ( F. /\ F. ) <-> F. )
5	3, 4	xchnxbir 676	. . 3 |- ( -. ( F. /\ F. ) <-> T. )
6	2, 5	anbi12i 457	. 2 |- ( ( ( F. \/ F. ) /\ -. ( F. /\ F. ) ) <-> ( F. /\ T. ) )
7		falantru 1398	. 2 |- ( ( F. /\ T. ) <-> F. )
8	1, 6, 7	3bitri 205	1 |- ( ( F. \/_ F. ) <-> F. )

Syntax hints:   -. wn 3   /\ wa 103   <-> wb 104   \/ wo 703   T. wtru 1349   F. wfal 1353   \/_ wxo 1370

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 609  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354  df-xor 1371

This theorem is referenced by: (None)