Proposition 16: If a variable x occurs in at least one of the statements \phi and \psi , then it occurs in the implication (\phi \Rightarrow \psi) .

Proof: Using (e) and (d) in the definition, x occurs in the negation \neg \psi , hence in the conjunction (\phi \wedge \neg \psi) , and thus in \neg (\phi \wedge \neg \psi) , i.e. in (\phi \Rightarrow \psi) . \square