 We saw in §2.2 that Conditional Proof (CP) is invalid for any conditional stronger than \(\supset\). It is invalid in Adams’s logic. For instance, “\({\sim}(A \amp B)\); \(A\); so \({\sim}B\)” is valid. It contains no conditionals. Any necessarily truth-preserving argument satisfies PPP. If I’m close to certain that I won’t be hit by a bomb and injured, and close to certain that I will be hit by a bomb, then I must be close to certain that I won’t be injured. But, as we saw, “\({\sim}(A \amp B)\); so \(A \Rightarrow{\sim}B\)” is invalid. Yet we can get the latter from the former by CP.