This is not a statement among many. It is the precondition for any statement. To deny A=A to say “a thing is not itself” – requires that the denial mean what it says and not its opposite. The act of denial assumes the identity of the words used. The attempt to reject identity performs identity. The axiom is inescapable.
If A=A is rejected, the rejection is incoherent. No symbol can refer stably to anything, including itself. The processor crashes.