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	⊢ ( 𝜑 ⊻ 𝜓 )
Assertion	axorbtnotaiffb	⊢ ¬ ( 𝜑 ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		axorbtnotaiffb.1	⊢ ( 𝜑 ⊻ 𝜓 )
2		df-xor	⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) )
3	1 2	mpbi	⊢ ¬ ( 𝜑 ↔ 𝜓 )