Muslims believe in the finality of prophethood because the revealed evidences are so numerous in number and decisive in wording that it leaves no doubt on the matter
The Qur'an for instance states the Prophet Muhammed is the "Seal of the Prophets" or the final prophet:
مَا كَانَ مُحَمَّدٌ أَبَآ أَحَدٍ مِّن رِّجَالِكُمْ وَلَكِن رَّسُولَ اللَّهِ وَخَاتَمَ النَّبِيِّينَ وَكَانَ اللَّهُ بِكُلِّ شَىْءٍ عَلِيماً Muhammad is not the father of any of your men, but he is the Apostle of Allah and the Last of the prophets; and Allah is cognizant of all things. (33:40)
and Muslims believe that the Qur'an is the revealed word of God that has been preserved in its original form.
A number of ahadith make the same point:
Sa'd narrated the Prophet (saw) said to Ali (ra): "You are to me as Harun was to Musa except that there is no prophet after me." (Muslim)
Abu Huraira narrated the Prophet (saw) said, "The children of Israel were ruled and guided by prophets. Whenever a prophet died, another would take over his place. There will be no more prophets after me, but there will be Caliphs who grow in number." (Bukhari)
Abu Huraira narrated the Prophet (saw) said, "There is no prophet between me and him, that is, Jesus (as)." (Abu Dawud)
The Prophet (saw) said, "In my Ummah there shall be thirty great liars (Dajjals), each of whom will claim to be a prophet. I am the last prophet; there will be no prophet after me." (Abu Dawood, Tirmidhi)
Abu Huraira narrated the Prophet (saw) said, "I have been sent for all the people of the world and prophethood has ended with me." (Tabaqat al-Kubra)
Finally the companions are narrated to have made similar points. Umar ibn al-Khattab whilst he was a caliph made a clear statement when Musaylamah was killed that it was due to his claim of being a prophet as after Muhammed there were no other messengers. No companion questioned or disputed this matter and allowed capital punishment to be applied.
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