  We show that in $L(\mathbb{R})$, assuming large cardinals, $\mathsf{HOD}
{\parallel}\eta^{+\mathsf{HOD}}$ is locally definable from $\mathsf{HOD}
{\parallel}\eta$ for all $\mathsf{HOD}$-cardinals $\eta\in
[\boldsymbol{\delta}^2_1,\Theta)$. This is a further elaboration of the
statement "$\mathsf{HOD}^{L(\mathbb{R})}$ is a core model below $\Theta$" made
by John Steel.
