Is the extender embedding from an I1 embedding necessarily an I2 embedding

Question

If we suppose that $\kappa$ is the critical point of an $I_1$ elementary embedding $j$ and that $\lambda$ is the supremum of the critical sequence of $j$ and we consider the $(\kappa,\lambda)$-extender embedding derived from $j$, is there some well-known reference for a proof that this extender embedding is necessarily an $I_2$ embedding, or is this perhaps something ridiculously easy to see that I am missing through my own stupidity?