Now that I have explained all necessary conditions of prophet-hood, it will not be out of place to give in short sentences some proofs of the Divine origin of the prophethood of the Holy Prophet of Islam, Muhammad Mustafa (s.a.w.).
First Proof: Everybody knows that Prophet Muhammad Mustafa (s.a.w.) claimed to be the Prophet from Allah; and he showed miracles in support of that claim. It proves that his claim was right.
Now this proof can be multiplied by 4000, mentioning each Mu-jiza separately. Therefore, this one proof is potentially 4000 proofs.
Second Proof: Previous prophets had prophesied that the last prophet would appear in Arabia; and he will testify to the truth of the previous prophets; and' many of the prophecies mentioned his personal qualities and attributes and gave details of his family life. Prophet Muhammad Mustafa (s.a.w.) claimed to be that prophet; and all the details fitted him perfectly.
It proves that his claim was right.
This proof can be multiplied by, say 100, giving each prophecy separately. Therefore, this one proof contains potentially about 100 proofs.
Thirdly Proof: Prophet Muhammad Mustafa (s.a.w.) was born in a country whose people were nomads of desert, who spent their lives in tribal warfare, plunder and killing. They did not know what knowledge was; the only discipline they observed was the discipline of self-preservation.
In such a country, and in such a people, an orphaned child is born and is cared for by his grandfather and then by his uncle; does not know what a book is and nobody teaches him how to write even the alphabets. He spends more than half of his life in trade and commerce.
And then, all of a sudden, that son of desert claims that he has brought an everlasting universal law of the whole mankind for all the days to come.
And that law proves to be so perfect, so admirable and so much before his time that the world, even after fourteen hundred years is gasping to catch with it. The history of Law and Shariah in the last 14 centuries can be described in one sentence: "Islam leads and the world trails behind."
Is not that perfection of the Shariah, with its built-in capacity to adjust according to time, the greatest miracle of the Holy Prophet?
A Muslim thinker of the last century has written that a Christian priest asked him the proof of the truth of the Holy Prophet. He enumerated some of the proofs. At last, the Christian priest said: "My friend, the greatest proof of the Divine origin of Islam is in the absolute perfection of its Shariah. People in my country (England) elect their representatives; those representatives are supposed to be the cream of the society.
The parliament consists of the elite of the country. They bring forth a bill; they discuss it for days and even weeks and months; they amend it and mould it in the background of their life-long experiences. Then, Jo! no sooner is the bill enacted than a new situation crops up and an amendment is brought up to make that legislation up-to-date. And look at the Shariah of Islam, which has maintained its originality since last 13 (now, 14) centuries and nobody has been able to say that this or that law needs amendment.
"This eternity is the best and finest proof of the truth of the Prophet of Islam.”

Last Prophet
Here I am giving a few references to show that the Holy Prophet of Islam was the Last Prophet, and no prophet is to come after him:
1. The Holy Prophet said, "Bani Israel, prophets were leading them; when a prophet died another prophet succeeded him. But after me there will be no prophet; there will be Khalifas."

كانت بنو اسرائيل تسوسهم انبياء كلما هلك نبي خلفه نبي وانه لا نبي بعدي وسيكون خلفاء

It clearly shows that there is no room for any new prophet to come after the Holy Prophet of Islam.
2. The Holy Prophet said, "The example of myself and the prophets who proceeded me is the example of a man who built a very beautiful building, but there was a brick missing in one corner. People were going round that building and wondering on the beauty of that building; but all the same they were saying why no brick was put in that place. Thus, I am that brick which was missing and I have been put in that place and I am 'Khatamun-Nabiyyin.’

قال رسول الله صلى الله عليه وآله: مثلي ومثل الانبياء كمثل قصر أحسن بنيانه ترك منه موضع لبنة فطاف به النظار يتعجبون من حسن بنيانه الا موضع تلك اللبنة فكنت انا سددت موضع اللبنة ختم بي البنيان وختم بي الرسل فانا اللبنة وانا خاتم النبيين

It means that after the advent of the Holy Prophet of Islam, the building of Prophethood was complete; there was no vacant place left, so that another Prophet be expected to come and fill that place
3. The Holy Prophet said: Quiyamat will not come till many groups from my Ummat follow the idol-worshippers (commit capital sins like the idol-worshippers) and till they worship idols; and surely there will be in my Ummat 30 imposters, everyone of them will suppose himself to be a prophet; while I am 'Khatamun-Nabiyyin' (last prophet) there is no prophet after me."

قال رسول الله صلى الله عليه واله: لاتقوم الساعة حتى تلحق قبائل من امتي بالمشركين وحتى يعبدوا
الوثن وانه سيكون في امتي ثلاثون كذابون كلهم يزعم انه نبي وانا خاتم النبيين لانبي بعدي

4. Imam Ali (a.s.) said when he was washing the body of the Holy Prophet (s.a.w.): "My father and mother be your ransom, such a thing has been discontinued with your death which was never discontinued with the death of any other person. (And that thing is) Prophethood, announcement of Ghaib and the news of heaven."

ومن كلام له عليه السلام قاله وهو يلي غسل رسول الله صلى الله عليه واله وتجهيزه: بأبي انت وامي لقد
انقطع بموتك ما لم ينقطع بموت غيرك من النبوة والأنباء واخبار السماء

Names and Titles of The Holy Prophet
The following names and titles of the Holy Prophet of Islam are taken from the Qur'an:

Name in Arabic Translitteration Meaning
محمد Muhammad The Most Praiseworthy
احمد Ahmad The greatest Glorifyer
رحمة للعالمين (Rehmatun Lil-Aalameen( The Mercy for the Universe
رسول الله Rasul-ul-lah Messenger of Allah
النبي An-Nabi The Prophet
البشير AI-Bashir The Bringer of good Tidings
النذير An-Nadhir The Warner
النور An-Nur The Light
الميزان AI-Mizan The Scale (of equality)
المزمل AI-Muzzammil The Wrapped
المدثر AI-Muddaththir The Covered
السراج المنير As-Sirajul-Mumir The Brightening Lamp
الشاهد As-Shahid The Witness
الشهید As-Shaheed The Witness
الداعي الى الله Ad-Dai ila-Allah The Caller to Allah
اول المسلمين Awwal-ul-Muslimeen
The First Muslim
اول العابدين Awwa!-ul-Abedin The First Worshipper
خاتم النبيين Khatam-un- Nabiyyin The Seal of the Prophets, the last Prophet, the Leader
يس – طه Ya-Sin, Ta-Ha The Purified