Sahih Bukhari Volume 5, Book 59, Hadith Number 736.

Narrated By Al-Aswad : It was mentioned in the presence of ‘Aisha that the Prophet had appointed ‘Ali as successor by will. Thereupon she said, “Who said so? I saw the Prophet, while I was supporting him against my chest. He asked for a tray, and then fell on one side and expired, and I did not feel it. So how (do the people say) he appointed ‘Ali as his successor?”