Now it is self-evident that
AD = AD,
and in one side of this identity we may for A substitute its equivalent B ꖌ C, obtaining
AD = BD ꖌ CD.
Since “a gaseous element is either hydrogen, or oxygen, or nitrogen, or chlorine, or fluorine,” it follows that “a free gaseous element is either free hydrogen, or free oxygen, or free nitrogen, or free chlorine, or free fluorine.”
This process of combination will lead to most useful inferences when the qualifying adjective combined with both sides of the proposition is a negative of one or more alternatives. Since chlorine is a coloured gas, we may infer that “a colourless gaseous element is either (colourless) hydrogen, oxygen, nitrogen, or fluorine.” The alternative chlorine disappears because colourless chlorine does not exist. Again, since “a tooth is either an incisor, canine, bicuspid, or molar,” it follows that “a not-incisor tooth is either canine, bicuspid, or molar.” The general rule is that from the denial of any of the alternatives the affirmation of the remainder can be inferred. Now this result clearly follows from our process of substitution; for if we have the proposition
A = B ꖌ C ꖌ D,
and we insert this expression for A on one side of the self-evident identity
Ab = Ab,
we obtain Ab = ABb ꖌ AbC ꖌ AbD;