"There is at most one student" is symbolized as
$(\forall x)(Sx \to (\forall y)(Sy \to x=y)$

Earlier I asked this question [$(\forall x)[Mx -> (\forall y)(My -> Kxy)]$, can $x\;\&\; y$ be the same thing?](https://math.stackexchange.com/questions/3517211/forall-xmx-forall-ymy-kxy-can-x-y-be-the-same-thing)

and they told me that x and y can be the same thing. Now in confused because I would read the statement above as "for everything, if it's a student, then, for everything else if it's a student, then they have to be the same student" which it would make sense. But if x and y can be the same I don't understand how I should interpret it. Could you guys help please?