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 Categorical Syllogism with two Negative Premises is Valid

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