Proposition 12: If a variable x occurs in at least one of the statements \phi and \psi , then it occurs in the disjunction (\phi \vee \psi) .

Proof: By (e) in the definition, x occurs in the negation \neg \phi and \neg \psi . Then, using (d), x occurs in the conjunction (\neg \phi \wedge \neg \psi) . Using (e) again, x occurs in \neg (\neg \phi \wedge \neg \psi) , for which (\phi \vee \psi) is shorthand. \square