What is a good reference for the following fact (the hypotheses may not be quite right):

Let $X$ and $Y$ be projective varieties over a field $k$. Let $\mathcal{F}$ and $\mathcal{G}$ be coherent sheaves on $X$ and $Y$, respectively. Let $\mathcal{F} \boxtimes \mathcal{G}$ denote $p_1^*(\mathcal{F}) \otimes_{\mathcal{O}_{X \times Y}} p_2^* \mathcal{G}$. Then $$H^m(X \times Y, \mathcal{F} \boxtimes \mathcal{G}) \cong \bigoplus_{p+q=m} H^p(X,\mathcal{F}) \otimes_k H^q(Y, \mathcal{G}).$$

Note: Wikipedia leads me to believe that this may be related to Theorem 6.7.3 in EGA III_{2}, but I find this theorem quite intimidating. Although I would be willing to study this if there is no more basic reference, I would at least like some confirmation that I am studying the right thing.