# “Reverse” application of Riesz representation theorem

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?