Determine whether this statement is true or false

Question

I have a statement

A: "$\forall x, \exists y$ such that $\forall z, x + y = z$."

I can find a $y$ for all $x$ and $z$ such that $y = z -x$.

But this $y$ is not fixed for all $x$ and $z$.

Hence A is $false$.

Can you verify?