Product measure and measurability

Let $(X,\mathcal{G})$ and $(Y,\mathcal{H})$ be measure spaces, and $f:X\times Y\rightarrow \mathbb{R}$ be measurable with respect to the product measure space $(X\times Y,\sigma(\mathcal{G}\times\mathcal{H}))$.

Show that $x\mapsto f(x,y)$ is a Borel measurable function.

Any help is greatly needed