Iput in a nonpermanent hairdye brownblack 1week ago.can i go on &put in a permanentdye of a darkercolor overit?

I heard that if you put in a permanent dye over a non-permanent dye before the non-permanent dye washes out, when the non-permanent dye does wash out the permanent dye will wash out with it and your hair will get lighter. Is this true? I really want to go on and put in the permanent dye of the darker color because this non-permanent dye is already fading! It's dark brown now by the way and im just gonna make it darker. Sorry, kind of confusing and lots of repetition of the same words.