The Messenger of Allah ﷺ did not promise us anything on which we might base a claim of succession, rather it is something that we thought of ourselves, then Abu Bakr was appointed as his successor; may the mercy of Allah be upon Abu Bakr, for he did well and remained steadfast. Then ‘Umar was appointed as his successor, may the mercy of Allah be upon ‘Umar, for he did well and remained steadfast, until the religion of Islam became well established.  

أَنَّهُ قَالَ يَوْمَ الْجَمَلِ إِنَّ رَسُولَ اللهِ ﷺ لَمْ يَعْهَدْ إِلَيْنَا عَهْدًا نَأْخُذُ بِهِ فِي إِمَارَةٍ وَلَكِنَّهُ شَيْءٌ رَأَيْنَاهُ مِنْ قِبَلِ أَنْفُسِنَا ثُمَّ اسْتُخْلِفَ أَبُو بَكْرٍ رَحْمَةُ اللهِ عَلَى أَبِي بَكْرٍ فَأَقَامَ وَاسْتَقَامَ ثُمَّ اسْتُخْلِفَ عُمَرُ رَحْمَةُ اللهِ عَلَى عُمَرَ فَأَقَامَ وَاسْتَقَامَ حَتَّى ضَرَبَ الدِّينُ بِجِرَانِهِ