Distributed Term of Conclusion of Valid Categorical Syllogism is Distributed in Premise

Theorem
Let $T$ be a term of the conclusion $C$ of a valid categorical syllogism $Q$.

Let $T$ be distributed in $C$.

Then $T$ is also distributed in whichever premise of $Q$ in which it appears.

Also see

 * Rules of Quantity
 * Middle Term of Valid Categorical Syllogism is Distributed at least Once

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