Is the Prophet Muhammad (peace be upon him) described as a prophet and a caliph?

If the intention behind describing the Prophet, peace and blessings be upon him, as the 'Khalifa of Allah on His earth' is understood, then there is no legal impediment to this, despite the absence of an explicit textual reference with this specific wording in revelation. Allah the Almighty has indeed described some of His prophets as having vicegerency (khilafa) on earth, such as David, peace be upon him, and commanded them to judge among people with justice. Similarly, the Prophet, peace and blessings be upon him, was commanded to judge according to what Allah revealed, and he was the Imam of the Muslims, the head of their state, and their judge with justice. All of this was by the command and revelation of Allah, which makes him worthy of this description.