Studies and Exercises in Formal Logic - John Neville Keynes

	All S is S,	by the law of identity,
and	Some S is not-P,	byobversion of the given proposition,
therefore,	Some not-P is S.

It will be found that, adopting the same method, the contraposition of E is yielded by a syllogism in Darapti.

(4) We might also obtain the contrapositive of All S is P as follows:—

By the law of excluded middle, All not-P is S or not-S, and, by hypothesis, All S is P,

therefore,	All not-P is P or not-S ;
but, by the law of contradiction,	No not-P is P,
therefore,	All not-P is not-S.[163]

[¹⁶³] Compare Jevons, Principles of Science, chapter 6, § 2; and Studies in Deductive Logic, p. 44.

153 (5) The contraposition of A may also be established indirectly by means of a syllogism in Darii:—

	All S is P,
therefore,	No not-P is S ;

for, if not, Some not-P is S ; and we have the following syllogism,—