Is $\sf V=HOD$ a theorem of $\sf ZF + V=L$?
[EDIT:] I'm not really sure if adding the following, somewhat personal, motivation would be helpful, but that what was really occurring to my mind. The context of this question is that I was thinking of the concept of all sets being parameter free definable (see: Definability rule) as a concept that confers concreteness to the notion of set, then to foster this line I was thinking of adding the notion of constructibility as well, and thus advocate $\sf ZF + [V=L] + Definability$ as a concrete kind of set theory. I was wondering about what can $\sf Definability$ add to $\sf ZF+[V=L]$? I came to know that it proves $\sf V=HOD$, and didn't know if that is already a theorem of $\sf ZF + [V=L]$. More generally, the question is related to what natural statements we can find outside of Godel's constructible realm and especially those that can be captured if we add definability to it.
Yes, by the definability of the $L$-ordering. If $M\models\mathsf{ZF+V=L}$, then for each $m\in M$ there is some $M$-ordinal $\alpha$ such that $m$ is the unique thing which $M$ thinks is the $\alpha$th object in the $L$-ordering; this is a definition of $m$ wth an ordinal parameter, so $m\in\mathsf{OD}^M$.
Alternatively, as a nuke you can use the fact that $\mathsf{HOD}$ is an inner model and $L$ is the minimal inner model.