 Conditional Proof seems sound: “From \(X\) and \(Y\), it follows that \(Z\). So from \(X\) it follows that if \(Y, Z\)”. Yet for no reading of “if” which is stronger than the truth-functional reading is CP valid — at least this is so if we treat “&amp;” and “\({\sim}\)” in the classical way and accept the validity of the inference: (I) \({\sim}(A \amp{\sim}B)\); \(A\); therefore \(B\). Suppose CP is valid for some interpretation of “If \(A, B\)”. Apply CP to (I), and we get \({\sim}(A \amp{\sim}B)\); therefore if \(A, B\), i.e., \(A \supset B\) entails if \(A, B\).