Rules for Valid Syllogisms

1. If a syllogism is valid, then the middle term is distributed at least once.
2. If a syllogism is valid, then if a term is distributed in the conclusion, it must be distributed in a premise.
3. If a syllogism is valid, it does not have two negative premises.
4. If a syllogism is valid, then it has a negative premise, if and only if it has a negative conclusion.
5. If a syllogism is valid, then if its premises are universal, then its conclusion is universal.