In a lot of places equality is defined that for two expressions A=B, A=B means that A and B have the same value (A=B). This relationship seems strange as we are slightly abusing use/mention, if '=' denotes a relationship between expressions then in '1+1=2' '1+1' and '2' are denoting themselves.
Doing this seems a little bit strange considering we generally use '2' and '1+1' to denote values themselves.
If we treat equality as a relationship a mathematical object has with itself, it is not that useful, however the variety of the names and what they inform us of is, for example x+1=2 is equivalent to 2=2 but the former is more interesting.
In this way, is the elementary mathematical use of the equals sign essentially just an identity statement? (Ignoring the intricacies of the idea that different objects that we equate aren't always mathematically the same due to their construction, as I usually get linked this article and it's not really what I'm asking).