Non-Equivalence as Conjunction of Disjunction with Negation of Conjunction

Theorem

 * $\neg \paren {p \iff q} \dashv \vdash \paren {p \lor q} \land \neg \paren {p \land q}$

That is, negation of the biconditional means the same thing as either-or but not both, that is, exclusive or.