Deduction of $\forall y \exists x (x=y)$ Give a deduction of $\forall y \exists x (x=y)$

My thinking is I can prove $\exists x(x=y)$ then use generalization theorem，
which is equivalent to prove $\neg \forall x \neg (x=y)$ but I got stuck proving this...
thanks in advance

Sorry that I did not specify what deduction system that I want to use here, it is the deduction sequence  where ai is either Axiom or original hypothesis or obtained from MP
Hint:

$$\matrix{ y=y \\ \hline \exists x.x=y \\
\hline 
\forall y.\exists x.x=y } $$
For any arbitrary value $v$, because we always witnesses $v=v$ by the Law of Identity, therefore ...

Since this is so for any arbitrary value , then we deduce ...

$\blacksquare$.