From Cantor's Attic:

A cardinal κ is a Berkeley cardinal, if for any transitive set $M$ with $κ∈M$ and any ordinal $α<κ$ there is an elementary embedding $j : M → M$ with $\alpha<\text{crit}(j)<\kappa$. These cardinals are defined in the context of ZF set theory without the axiom of choice.

I have seen claimed several times that the existence of a Berkeley is stronger than that of a Reinhardt cardinal (let's say in NBG without Choice, as formalizing existence of Reinhardts in ZF takes some extra consideration). I can't however find any proof of this claim.

Of course if Berkeley-ness were about elementary embeddings of arbitrary classes containing $\kappa$, then it would be obvious, but we are only talking about transitive set models here, so I don't really see what to do. Can anyone provide a proof that Berkeley are stronger than Reinhardts? What about Super Reinhardts?