Theorem excxor 1469

Description: This tautology shows that xor is really exclusive. (Contributed by FL, 22-Nov-2010.)

Assertion

Ref	Expression
excxor	|- ( ( ph \/_ ps ) <-> ( ( ph /\ -. ps ) \/ ( -. ph /\ ps ) ) )

Proof of Theorem excxor

Step	Hyp	Ref	Expression
1		df-xor 1465	. 2 |- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
2		xor 935	. 2 |- ( -. ( ph <-> ps ) <-> ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) )
3		ancom 466	. . 3 |- ( ( ps /\ -. ph ) <-> ( -. ph /\ ps ) )
4	3	orbi2i 541	. 2 |- ( ( ( ph /\ -. ps ) \/ ( ps /\ -. ph ) ) <-> ( ( ph /\ -. ps ) \/ ( -. ph /\ ps ) ) )
5	1, 2, 4	3bitri 286	1 |- ( ( ph \/_ ps ) <-> ( ( ph /\ -. ps ) \/ ( -. ph /\ ps ) ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383   /\ wa 384   \/_ wxo 1464

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-xor 1465

This theorem is referenced by:  f1omvdco2  17868  psgnunilem5  17914  or3or  38319