 Aristotle holds that an assertoric syllogism remains valid if “necessarily” is added to its premises and its conclusion: the modal pattern \(NNN\) is always valid. He does not treat this as a trivial consequence but instead offers proofs; in all but two cases, these are parallel to those offered for the assertoric case. The exceptions are Baroco and Bocardo, which he proved in the assertoric case through impossibility: attempting to use that method here would require him to take the denial of a necessary \(O\) proposition as hypothesis, raising the complication noted above, and he uses the procedure he calls ecthesis instead (see Smith 1982).