Like, if I have "A & B" then I can deduce that "A". — MindForged

Yeah, but only if you're following the rule that in any given conversation, the symbol (or rather, identity, essence) "A" shall always be proposed for some particular object, not other objects, and not all objects.

It's just the form of "A=A" that's misleading, it looks like a truth about the world is being revealed - but as I said, what real relation in the world is "is identical with"? Nothing, there's no relation in the real world that answers to that description.

"Is identical with" only means that the hypothetical identity (essence or nature) symbolized by "A" shall (in any given conversation) be proposed to be the identity of some particular object singled out in experience, and not other objects, and not the whole of experience.

This is how thought (and common sense/experiment) works: we punt identities for things, and see whether things answer to those identities (whether our subsequent experience is what we'd expect if the object actually has that identity or nature). But in order to do so, the most fundamental prerequisite is that we have to track objects with one singular identity in the course of our investigations. This is so that we can match our expectations (set up by that proposed identity) from the past, with what eventuates now or in the future - with what's given by experience, if we've worked with the assumption that the thing has that identity.