Conclusion of Valid Categorical Syllogism is Negative iff one Premise is Negative

Theorem
The conclusion of a valid categorical syllogism is negative iff one of the premises is also negative.

Also see

 * Rules of Quality
 * No Valid Categorical Syllogism contains two Negative Premises

Historical Note
This rule of quality was axiomatic at the time of Aristotle, when the theory of the categorical syllogism was initially developed.