Theorem xor2

Description: Two ways to express "exclusive or". (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Assertion	xor2	|- ( ( ph \/_ ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		df-xor	|- ( ( ph \/_ ps ) <-> -. ( ph <-> ps ) )
2		nbi2	|- ( -. ( ph <-> ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )
3	1 2	bitri	|- ( ( ph \/_ ps ) <-> ( ( ph \/ ps ) /\ -. ( ph /\ ps ) ) )