Sahih al-Bukhari 4459
Narrated Al-Aswad:
It was mentioned in the presence of `Aisha that the Prophet (ﷺ) 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?"
حَدَّثَنَا عَبْدُ اللَّهِ بْنُ مُحَمَّدٍ، أَخْبَرَنَا أَزْهَرُ، أَخْبَرَنَا ابْنُ عَوْنٍ، عَنْ إِبْرَاهِيمَ، عَنِ الأَسْوَدِ، قَالَ ذُكِرَ عِنْدَ عَائِشَةَ أَنَّ النَّبِيَّ صلى الله عليه وسلم أَوْصَى إِلَى عَلِيٍّ، فَقَالَتْ مَنْ قَالَهُ لَقَدْ رَأَيْتُ النَّبِيَّ صلى الله عليه وسلم وَإِنِّي لَمُسْنِدَتُهُ إِلَى صَدْرِي، فَدَعَا بِالطَّسْتِ فَانْخَنَثَ فَمَاتَ، فَمَا شَعَرْتُ، فَكَيْفَ أَوْصَى إِلَى عَلِيٍّ