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[Hadji]

Sahih Muslim
Book 31, Number 5955:


'A'isha reported that Allah's Apostle (may peace be upon him) went out one norning wearing a striped cloak of the black camel's hair that there came <b>Hasan b. 'Ali.</b> He wrapped hitn under it, then came <b>Husain</b> and he wrapped him under it along with the other one <b>(Hasan)</b>. Then came <b>Fatima</b> and he took her under it, then came <b>'Ali</b> 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, and purify you (thorough purifying)


http://www.iiu.edu.my/deed/hadith/muslim/031_smt.html

Al-Husain, Al-Hassan, Fatima, Ali, and Mohammed (pbuh) are all considered to be from Ahlulbayt. I agree with that.

Sunan Tirmidhi
The verse "Verily Allah intends to ... (33:33)" was revealed to the Prophet (PBUH&HF) in the house of Umm Salama. Upon that, the Prophet gathered Fatimah, al-Hasan, and al-Husain, and covered them with a cloak, and he also covered Ali who was behind him. Then the Prophet said: "O' Allah! These are the Members of my House (Ahlul-Bayt). Keep them away from every impurity and purify them with a perfect purification." <b>Umm Salama (the wife of Prophet) asked: "Am I also included among them O Apostle of Allah?" the Prophet replied: "You remain in your position and you are toward a good ending."</b>

This hadeeth is different from the other one. Umm Salama wasn't a part of the first hadeeth. I looked up the link you've provided and here is what I found under the same hadeeth.


قَالَ هَذَا حَدِيثٌ غَرِيبٌ مِنْ هَذَا الْوَجْهِ مِنْ حَدِيثِ عَطَاءٍ عَنْ عُمَرَ بْنِ أَبِي سَلَمَةَ ‏.


The hadeeth is not authentic.

However in the other hadith he clearly says that the wives are NOT included in AhlulBayt.

Scroll to the top of the page. The Prophet (pbuh) considers A'isha to be from ahlul-bayt. Are you going to accept the definition of Mohammed (pbuh) or the companion?

Since my arabic is way out of its depth you'll have to wait a few days for an answer to that question.

Please try to be objective while researching this topic. I advise you to use your proper judgement instead of just accepting any Shi'ite response.