Source: A Concise Introduction to Logic (12 Ed, 2014), by Patrick J. Hurley
[p 286:] Rule 1: The Middle Term Must Be Distributed at Least Once.
[p 288:] Rule 4: A Negative Premise Requires a Negative Conclusion,
and a Negative Conclusion Requires a Negative Premise.[p 288:] Rule 5: If Both Premises Are Universal, the Conclusion Cannot Be Particular.
[p 290:] [...] The question remains, however, whether a syllogism’s breaking none of the rules is a sufficient condition for validity. In other words, does the fact that a syllogism breaks none of the rules guarantee its validity? The answer to this question is “yes,” but unfortunately there appears to be no quick method for proving this fact. [...] The proof that follows is somewhat tedious, and it proceeds by considering four classes of syllogisms having A, E, I, and O propositions for their conclusions. [...]
[p 291:] Next, consider a syllogism having an I proposition for its conclusion.
By Rule 1, M is distributed in at least one premise,
and by Rule 4, both premises are affirmative.
Further, by Rule 5, both premises cannot be universal. [...]
I do not comprehend only the step bolded above:
How does Rule 4 imply that both premises must be affirmative?
