A'isha identifies who the members of the AhlulBayt are, and who was purified in Quran 33:33

Reference: Sahih Muslim 2424

Sahih Muslim 2424
`A'isha reported:

that Allah's Apostle (ﷺ) went out one norning wearing a striped cloak of the black camel's hair that there came Hasan b. 'Ali. He wrapped hitn under it, then came Husain and he wrapped him under it along with the other one (Hasan). Then came Fatima and he took her under it, then came 'Ali and he also took him under it and then said:

Allah only desires to take away any uncleanliness from you, O people of the household (AhlulBayt), and purify you (thorough purifying) - (Quran 33:33)

حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ، وَمُحَمَّدُ بْنُ عَبْدِ اللَّهِ بْنِ نُمَيْرٍ، - وَاللَّفْظُ لأَبِي بَكْرٍ - قَالاَ حَدَّثَنَا مُحَمَّدُ بْنُ بِشْرٍ، عَنْ زَكَرِيَّاءَ، عَنْ مُصْعَبِ بْنِ شَيْبَةَ، عَنْ صَفِيَّةَ بِنْتِ شَيْبَةَ، قَالَتْ قَالَتْ عَائِشَةُ خَرَجَ النَّبِيُّ صلى الله عليه وسلم غَدَاةً وَعَلَيْهِ مِرْطٌ مُرَحَّلٌ مِنْ شَعْرٍ أَسْوَدَ فَجَاءَ الْحَسَنُ بْنُ عَلِيٍّ فَأَدْخَلَهُ ثُمَّ جَاءَ الْحُسَيْنُ فَدَخَلَ مَعَهُ ثُمَّ جَاءَتْ فَاطِمَةُ فَأَدْخَلَهَا ثُمَّ جَاءَ عَلِيٌّ فَأَدْخَلَهُ ثُمَّ قَالَ ‏{‏ إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا‏}‏‏
Reference  : Sahih Muslim 2424
In-book reference  : Book 44, Hadith 91
 
Corroborating Reference from the step-son of Rasulullah(ﷺ):
Jami` at-Tirmidhi 3205
Narrated 'Umar bin Abi Salamah - the step-son of the Prophet (ﷺ):

"When these Ayat were revealed to the Prophet (ﷺ): 'Allah only wishes to remove the Rijs from you, O members of the family, and to purify you with a thorough purification (33:33)' in the home of Umm Salamah, he called for Fatimah, Hasan, Husain, and wrapped him in the cloak, and 'Ali was behind him, so he wrapped him in the cloak, then he said: 'O Allah! These are the people of my house, so remove the Rijs from them, and purify them with a thorough purification.' So Umm Salamah said: 'And I, Prophet of Allah?' He said: 'You are in your place and you are goodness.'"

حَدَّثَنَا قُتَيْبَةُ، حَدَّثَنَا مُحَمَّدُ بْنُ سُلَيْمَانَ بْنِ الأَصْبَهَانِيِّ، عَنْ يَحْيَى بْنِ عُبَيْدٍ، عَنْ عَطَاءِ بْنِ أَبِي رَبَاحٍ، عَنْ عُمَرَ بْنِ أَبِي سَلَمَةَ، رَبِيبِ النَّبِيِّ صلى الله عليه وسلم قَالَ لَمَّا نَزَلَتْ هَذِهِ الآيَةُ عَلَى النَّبِيِّ صلى الله عليه وسلمَّ ‏:‏ ‏(‏ إنمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا ‏)‏ فِي بَيْتِ أُمِّ سَلَمَةَ فَدَعَا فَاطِمَةَ وَحَسَنًا وَحُسَيْنًا فَجَلَّلَهُمْ بِكِسَاءٍ وَعَلِيٌّ خَلْفَ ظَهْرِهِ فَجَلَّلَهُمْ بِكِسَاءٍ ثُمَّ قَالَ ‏"‏ اللَّهُمَّ هَؤُلاَءِ أَهْلُ بَيْتِي فَأَذْهِبْ عَنْهُمُ الرِّجْسَ وَطَهِّرْهُمْ تَطْهِيرًا ‏"‏ ‏.‏ قَالَتْ أُمُّ سَلَمَةَ وَأَنَا مَعَهُمْ يَا نَبِيَّ اللَّهِ قَالَ ‏"‏ أَنْتِ عَلَى مَكَانِكِ وَأَنْتِ عَلَى خَيْرٍ ‏"‏ ‏.‏ قَالَ هَذَا حَدِيثٌ غَرِيبٌ مِنْ هَذَا الْوَجْهِ مِنْ حَدِيثِ عَطَاءٍ عَنْ عُمَرَ بْنِ أَبِي سَلَمَةَ ‏.‏
Reference  : Jami` at-Tirmidhi 3205
In-book reference  : Book 47, Hadith 257