Theorem excxor

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

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

Proof

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