Definition 18: We recursively define when a variable x occurs quantified in a statement.
(a) Base cases: For any statement \phi , the variable x occurs quantified in the existence statement \exists x \phi .
(b) Recursion: If x occurs quantified in \phi , then it occurs quantified in the negation \neg \phi .
(c) Recursion: If x occurs quantified in at least one of \phi and \psi , then it occurs quantified the conjunction (\phi \wedge \psi) .
(d) Recursion: Given a variable y , if x occurs quantified in \phi then x occurs quantified in \exists y \phi .