I have seen the following statement being used in different papers but never saw a proof:

If $f:X\rightarrow Y$ is a flat morphism between normal varieties and $\mathcal F$ is a reflexive sheaf on $Y$ (i.e. $\mathcal F^{\vee\vee}\cong\mathcal F$). Then the pull-back $f^*\mathcal F$ is a reflexive sheaf on $X$.

Does someone know an easy way to prove this or a paper or book where it is proven?