B—A C—B C—A
If possible, let the minor premiss be negative. Then the major must be affirmative (by Rule 5), [Footnote: This refers to the General Rules of Syllogism.] and the conclusion must be negative (by Rule 6). But the major being affirmative, its predicate is undistributed; and the conclusion being negative, its predicate is distributed. Now the major term is in this figure predicate both in the major premiss and in the conclusion. Hence there results illicit process of the major term. Therefore the minor premiss must be affirmative.
§ 609. Proof of Rule 2.—The major premiss must be universal.
Since the minor premiss is affirmative, the middle term, which is its predicate, is undistributed there. Therefore it must be distributed in the major premiss, where it is subject. Therefore the major premiss must be universal.
FIGURE II.
§ 610. Proof of Rule 1,—One or other premiss must be negative.
A—B C—B C—A
The middle term being predicate in both premisses, one or other must be negative; else there would be undistributed middle.
§ 611. Proof of Rule 2.—The conclusion must be negative.
Since one of the premisses is negative, it follows that the conclusion also must be so (by Rule 6).