Let H be a Hilbertspace, H' the Dualspace of H.
We know from Riesz representation theorem that for every $\phi \in H'$ there is exaclty one $y \in H$ such that
$\phi(x) = \langle x,y \rangle$ for every $x \in H$.
Now is it also possible that for a $\phi \in H'$ we find exactly one $y \in H$ such that
$f(y) = \langle f, \phi \rangle$ for every $f \in H'$ ?
If so, how does that follow from Riesz representation theorem?