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	$$⊢\left(\phi ⊻\psi \right)$$
Assertion	axorbtnotaiffb	$$⊢\neg \left(\phi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		axorbtnotaiffb.1	$$⊢\left(\phi ⊻\psi \right)$$
2		df-xor	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$
3	1 2	mpbi	$$⊢\neg \left(\phi \leftrightarrow \psi \right)$$