What is the evidence that Muhammad is the Seal of the Prophets and Messengers together, and not merely the Seal of the Prophets?

Scholars have differed on the distinction between a Prophet (Nabi) and a Messenger (Rasul). The majority view is that a Prophet is one to whom revelation is given but who is not commanded to convey it, while a Messenger is one to whom revelation is given and who is commanded to convey it. They agree that a Messenger is superior to a Prophet, and that every Messenger is a Prophet, but not every Prophet is a Messenger. Therefore, the fact that Prophet Muhammad (peace be upon him) is the Seal of the Prophets means that there will be no Messenger after him either, because prophethood is a prerequisite for messengership. This is affirmed by Ibn Kathir and Ibn Uthaymin, for the status of messengership is more specific than that of prophethood.