All A is AB may obviously be resolved into the two propositions All A is A, All A is B.[491] But the former of these is a merely identical proposition and gives no information. All A is AB is, therefore, equivalent to the simple proposition All A is B. Similarly, All AB is AC or DE is equivalent to All AB is C or DE.
[491] The resolution of complex propositions into a combination of relatively simple ones will be considered further in the following [section].
Again, Some A is not AB affirms that Some A is a or b ;[492] but by the law of contradiction No A is a ; therefore, Some A is not B, and obviously we can also pass back from this proposition to the one from which we started. Similarly, Some AB is not either AC or DE is equivalent to Some AB is not either C or DE.
[492] The process of obversion will be considered in detail in [chapter 3].
(3) In a universal affirmative or a particular negative proposition any alternant of the predicate may be indifferently introduced or omitted as an alternant of the subject.
If All A is B or C, then by the law of identity it follows that Whatever is A or B is B or C ; it is also obvious that we can pass back from this to the original proposition.
Again, if Some A or B is not either B or C, then since by the law of identity All B is B it follows that Some A is not either B or C ; and it is also obvious that we can pass back from this to the original proposition.
(4) In a universal affirmative or a particular negative proposition the contradictory of any determinant of the subject may be indifferently introduced or omitted as an alternant of the predicate, and vice versâ.
483 By this rule the three following propositions are affirmed to be equivalent to one another: All AB is a or C ; All B is a or C ; All AB is C ; and also the three following: Some AB is not either a or C ; Some B is not either a or C ; Some AB is not C.
The rule follows directly from rule (1) by aid of the process of obversion (see [chapter 3]).