Theorem xor3

Description: Two ways to express "exclusive or". (Contributed by NM, 1-Jan-2006)

	Ref	Expression
Assertion	xor3	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\phi \leftrightarrow \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		pm5.18	$$⊢\left(\phi \leftrightarrow \psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \neg \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \leftrightarrow \neg \psi \right)\leftrightarrow \neg \left(\phi \leftrightarrow \psi \right)$$
3	2	bicomi	$$⊢\neg \left(\phi \leftrightarrow \psi \right)\leftrightarrow \left(\phi \leftrightarrow \neg \psi \right)$$