A is A only because it is not B.
This would be the rational way of rendering the famous metaphysical claim.
Remove B, and A cannot be defined as A. Because A, in a vacuum of itself, has no comparative attributes…it is not relative to anything else, which means that A has no distinct location…for it is infinite. Its left is its right, its inside is its outside, its top is its bottom. And thus if A cannot be said to exist somewhere, it cannot be said to exist at all. Further, if A is A, and infinitely so, then it cannot be valued. It is…to an infinitely exclusive degree. It has exceeded the possibility of its own “existence”, again, to an infinite degree.
All of this is simply to say that is impossible to say what something (like A) is unless you know what it is not.
Therefore, A always and necessarily and absolutely implies B. A cannot exist, because it cannot be known or relevant, without a comparative and relative distinction from B.
This means that the claim that A is A is incomplete at best. At worst, it is a lie which ruins Truth.