Dark Magician of Chaos vs. Different Dimension Reincarnation

Ok... so I was wondering... In a situation such as this, am I right in thinking that regardless of the effect different dimension reincarnation has(if it were to be destroyed, destroy the equipped monster)Dark Magician of Chaos's effect would take priority over d.d.r and still be removed from play? Just looking for confirmation.
Thanks so much for your time!!!!!

Dark Magician of Chaos will still banished if it leaves the field, no matter how he got to the field or equipped with anything.

I just wanted to make sure I was right in thinking that under most circumstances, the monster effect would take priority. Ok... Thanks!!!!!

Like what already said above: It will still banished if leaves the field. Unless you had already activate a card like Imperial Iron Wall.