(x = A) entails xP
And we have now only to express the proposition that anything that has P, has also the property that P is internal to it. The required expression is obviously as follows. Just as "Anything that has Q, has R" is to be expressed by
xQ * xR
so "Anything that has P, has also the property that P is internal to it" will be expressed by
xP * {yP entails (y x)}
or by
xP * {(v x) entails yP}.
We have thus got, in the case of any particular property P, a means of expressing the proposition that it is internal to every term that possesses it, which is both short and brings out clearly the notions that are involved in it. And we do not need, I think, any further special convention for symbolising the proposition that every relational property is internal to any term which possesses it—the proposition, namely, which I called (2) above (pp. [289], [290]), and which on [p. 287], I called the most important consequence of the dogma of internal relations. We can express it simply enough as follows:—
(2) = "What we assert of P when we say xP * {yP entails (y = x)} can be truly asserted of every relational property."
And now, for the purpose of comparing (2) with (1), and seeing exactly what is involved in my assertion that (2) does not follow from (1), let us try to express (1) by means of the same conventions.