I am trying to find an explanation for the claim that the Eilenberg-Zilber theorem implies the isomorphism
$$\mathsf{Hom}_{\mathbf{sSet}}(\Delta\left[n\right] \times \Delta\left[1\right], L) \cong \mathsf{Hom}_{\mathbf{sSet}}(\Delta\left[n + 1\right], L),$$
where $\Delta\left[k\right]$ denotes the standard $k$-simplex.
I am familiar with the classical form of the theorem for singular chains, but I have been unable to use it for this isomorphism. Could anyone explain the proof for me or point me to a reference?