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

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## Contents

## Theorem

The conclusion of a valid categorical syllogism is negative if and only if one of the premises is also negative.

## Proof

## Also see

## Historical Note

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

## Sources

- 1965: E.J. Lemmon:
*Beginning Logic*... (previous) ... (next): $\S 4.4$: The Syllogism: Exercises: $\text{B}$: Rules of Quality: $1$