Does closing the bathroom prevent jinn from coming out into the rooms of the house?

Bathrooms are places where jinn and devils are abundant. The Prophet, peace and blessings be upon him, commanded us to close doors and mention the name of Allah over them at nightfall, because Satan does not open a closed door over which the name of Allah has been mentioned. Therefore, mentioning the name of Allah when closing the bathroom door prevents devils from entering the rest of the house's rooms.