 Here is a second argument in favour of Hook, in the style of Natural Deduction. The rule of Conditional Proof (CP) says that if \(Z\) follows from premises \(X\) and \(Y\), then “If \(Y, Z\)” follows from premise \(X\). Now the three premises \({\sim}(A \amp B), A\) and \(B\) entail a contradiction. So, by Reductio Ad Absurdum, from \({\sim}(A \amp B)\) and \(A\), we can conclude \({\sim}B\). So by CP, \({\sim}(A \amp B)\) entails “If \(A, {\sim}B\)”. Substitute “\({\sim}C\)” for \(B\), and we have a proof of “If \(A\), then \({\sim}{\sim}C\)” from “\({\sim}(A \amp{\sim}C)\)”. And provided we also accept Double Negation Elimination, we can derive “If \(A\), then \(C\)” from “\({\sim}(A \amp{\sim}C)\)”.