Theorem axorbtnotaiffb

Description: Given a is exclusive to b, there exists a proof for (not (a if-and-only-if b)); df-xor is a closed form of this. (Contributed by Jarvin Udandy, 7-Sep-2016)

	Ref	Expression
Hypothesis	axorbtnotaiffb.1	|- ( ph \/_ ps )
Assertion	axorbtnotaiffb	|- -. ( ph <-> ps )

Proof

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