Let's have a step by step approach to this argument:
Hadith Thaqalayn:
The Messenger of Allah (s) said: "Verily, I am leaving behind two precious things (thaqalayn) among you to which if you hold yourself, you will never astray:: the Book of God and my kindred (`itrah), my household (Ahl al-Bayt), for indeed, the two will never separate until they come back to me by the Pond (of al-Kawthar on the Day of Judgment).
1) As I said base on Hadith Thaqalayn we are supposed to adhere and follow 2 precious things 1.Quran 2. Hosuhold
2) As it obvious in the hadith if Muslims follow them they would never go astray .. so they are guidance .
3) These 2 heavy things have the same weights, one without the other one isn't helpful. Thus if we consider Quran as an intact pure and not distorted the same should be considered for the household as God confirmed it in his book through verse of Tathir :
33:33 Sahih International:
And abide in your houses and do not display yourselves as [was] the display of the former times of ignorance. And establish prayer and give zakah and obey Allah and His Messenger. Allah intends only to remove from you the impurity [of sin], O people of the [Prophet's] household, and to purify you with [extensive] purification.
The most important Q is who is the household of the prophet (pbuh):
Prophet (pbuh ) has answered it:
Therefore the households of the prophet(pbuh) is made up of 4 persons:
1) Imam Ali(as)
2) Lady Fatima(sa)
3) Imam Hassan
4) Imam Housain
And to make it clear that the verse addressing and talking about the wives of the prophet (pbuh) has got nothing with purification at the end of the verse and this part of verse is not about them I brought this document:
Then I brought the verse of Mobahele to show you who Prophet (pbuh) took by himself in this event, the verse says:
3:61 Sahih International:
Then whoever argues with you about it after [this] knowledge has come to you - say, "Come, let us call our sons and your sons, our women and your women, ourselves and yourselves, then supplicate earnestly [together] and invoke the curse of Allah upon the liars [among us]."
If you go read this event you will see who are those people ...
and regrading to your Q who is the household of the prophet ( which i don't know why you divert to another point)
حَدَّثَنِي زُهَيْرُ بْنُ حَرْبٍ وَشُجَاعُ بْنُ مَخْلَدٍ جَمِيعًا عَنْ ابْنِ عُلَيَّةَ قَالَ زُهَيْرٌ حَدَّثَنَا إِسْمَعِيلُ بْنُ
إِبْرَاهِيمَ حَدَّثَنِي أَبُو حَيَّانَ حَدَّثَنِي يَزِيدُ بْنُ حَيَّانَ قَالَ انْطَلَقْتُ أَنَا وَحُصَيْنُ بْنُ سَبْرَةَ وَعُمَرُ بْنُ
مُسْلِمٍ إِلَى زَيْدِ بْنِ أَرْقَمَ فَلَمَّا جَلَسْنَا إِلَيْهِ قَالَ لَهُ حُصَيْنٌ لَقَدْ لَقِيتَ يَا زَيْدُ خَيْرًا كَثِيرًا
رَأَيْتَ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَسَمِعْتَ حَدِيثَهُ وَغَزَوْتَ مَعَهُ وَصَلَّيْتَ خَلْفَهُ لَقَدْ
لَقِيتَ يَا زَيْدُ خَيْرًا كَثِيرًا حَدِّثْنَا يَا زَيْدُ مَا سَمِعْتَ مِنْ رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ قَالَ يَا
ابْنَ أَخِي وَاللَّهِ لَقَدْ كَبِرَتْ سِنِّي وَقَدُمَ عَهْدِي وَنَسِيتُ بَعْضَ الَّذِي كُنْتُ أَعِي مِنْ رَسُولِ اللَّهِ
صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ فَمَا حَدَّثْتُكُمْ فَاقْبَلُوا وَمَا لَا فَلَا تُكَلِّفُونِيهِ ثُمَّ قَالَ قَامَ رَسُولُ اللَّهِ صَلَّى
اللَّهُ عَلَيْهِ وَسَلَّمَ يَوْمًا فِينَا خَطِيبًا بِمَاءٍ يُدْعَى خُمًّا بَيْنَ مَكَّةَ وَالْمَدِينَةِ فَحَمِدَ اللَّهَ وَأَثْنَى عَلَيْهِ
وَوَعَظَ وَذَكَّرَ ثُمَّ قَالَ أَمَّا بَعْدُ أَلَا أَيُّهَا النَّاسُ فَإِنَّمَا أَنَا بَشَرٌ يُوشِكُ أَنْ يَأْتِيَ رَسُولُ رَبِّي فَأُجِيبَ
وَأَنَا تَارِكٌ فِيكُمْ ثَقَلَيْنِ أَوَّلُهُمَا كِتَابُ اللَّهِ فِيهِ الْهُدَى وَالنُّورُ فَخُذُوا بِكِتَابِ اللَّهِ وَاسْتَمْسِكُوا بِهِ
فَحَثَّ عَلَى كِتَابِ اللَّهِ وَرَغَّبَ فِيهِ ثُمَّ قَالَ وَأَهْلُ بَيْتِي أُذَكِّرُكُمْ اللَّهَ فِي أَهْلِ بَيْتِي أُذَكِّرُكُمْ اللَّهَ فِي
أَهْلِ بَيْتِي أُذَكِّرُكُمْ اللَّهَ فِي أَهْلِ بَيْتِي
فَقَالَ لَهُ حُصَيْنٌ وَمَنْ أَهْلُ بَيْتِهِ يَا زَيْدُ أَلَيْسَ نِسَاؤُهُ مِنْ
أَهْلِ بَيْتِهِ قَالَ نِسَاؤُهُ مِنْ أَهْلِ بَيْتِهِ وَلَكِنْ أَهْلُ بَيْتِهِ مَنْ حُرِمَ الصَّدَقَةَ بَعْدَهُ قَالَ وَمَنْ هُمْ قَالَ هُمْ
آلُ عَلِيٍّ وَآلُ عَقِيلٍ وَآلُ جَعْفَرٍ وَآلُ عَبَّاسٍ قَالَ كُلُّ هَؤُلَاءِ حُرِمَ الصَّدَقَةَ قَالَ نَعَمْ
و حَدَّثَنَا مُحَمَّدُ بْنُ بَكَّارِ بْنِ الرَّيَّانِ حَدَّثَنَا حَسَّانُ يَعْنِي ابْنَ إِبْرَاهِيمَ عَنْ سَعِيدِ بْنِ مَسْرُوقٍ
عَنْ يَزِيدَ بْنِ حَيَّانَ عَنْ زَيْدِ بْنِ أَرْقَمَ عَنْ النَّبِيِّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَسَاقَ الْحَدِيثَ بِنَحْوِهِ
بِمَعْنَى حَدِيثِ زُهَيْرٍ حَدَّثَنَا أَبُو بَكْرِ بْنُ أَبِي شَيْبَةَ حَدَّثَنَا مُحَمَّدُ بْنُ فُضَيْلٍ ح و حَدَّثَنَا إِسْحَقُ بْنُ
إِبْرَاهِيمَ أَخْبَرَنَا جَرِيرٌ كِلَاهُمَا عَنْ أَبِي حَيَّانَ بِهَذَا الْإِسْنَادِ نَحْوَ حَدِيثِ إِسْمَعِيلَ وَزَادَ فِي حَدِيثِ
جَرِيرٍ كِتَابُ اللَّهِ فِيهِ الْهُدَى وَالنُّورُ مَنْ اسْتَمْسَكَ بِهِ وَأَخَذَ بِهِ كَانَ عَلَى الْهُدَى وَمَنْ أَخْطَأَهُ
ضَلَّ حَدَّثَنَا مُحَمَّدُ بْنُ بَكَّارِ بْنِ الرَّيَّانِ حَدَّثَنَا حَسَّانُ يَعْنِي ابْنَ إِبْرَاهِيمَ عَنْ سَعِيدٍ وَهُوَ ابْنُ
مَسْرُوقٍ عَنْ يَزِيدَ بْنِ حَيَّانَ عَنْ زَيْدِ بْنِ أَرْقَمَ قَالَ دَخَلْنَا عَلَيْهِ فَقُلْنَا لَهُ لَقَدْ رَأَيْتَ خَيْرًا لَقَدْ
صَاحَبْتَ رَسُولَ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ وَصَلَّيْتَ خَلْفَهُ وَسَاقَ الْحَدِيثَ بِنَحْوِ حَدِيثِ أَبِي
حَيَّانَ غَيْرَ أَنَّهُ قَالَ أَلَا وَإِنِّي تَارِكٌ فِيكُمْ ثَقَلَيْنِ أَحَدُهُمَا كِتَابُ اللَّهِ عَزَّ وَجَلَّ هُوَ حَبْلُ اللَّهِ مَنْ
اتَّبَعَهُ كَانَ عَلَى الْهُدَى وَمَنْ تَرَكَهُ كَانَ عَلَى ضَلَالَةٍ وَفِيهِ
فَقُلْنَا مَنْ أَهْلُ بَيْتِهِ نِسَاؤُهُ قَالَ لَا وَايْمُ
اللَّهِ إِنَّ الْمَرْأَةَ تَكُونُ مَعَ الرَّجُلِ الْعَصْرَ مِنْ الدَّهْرِ ثُمَّ يُطَلِّقُهَا فَتَرْجِعُ إِلَى أَبِيهَا وَقَوْمِهَا أَهْلُ
بَيْتِهِ أَصْلُهُ وَعَصَبَتُهُ الَّذِينَ حُرِمُوا الصَّدَقَةَ بَعْدَهُ
قال بن كثير رحمه الله تعالى :
هكذا وقع في هذه الرواية،
والأولى أولى، والأخذ بها أحرى. وهذه الثانية تحتمل أنه أراد تفسير الأهل المذكورين في الحديث الذي رواه،
إنما المراد بهم آله الذين حُرموا الصدقة، أو أنه ليس المراد
بالأهل الأزواج فقط،
بل هم مع آله، وهذا الاحتمال أرجح؛ جمعا بينها وبين الرواية التي قبلها، وجمعا أيضا بين القرآن والأحاديث المتقدمة إن صحت، فإن في بعض أسانيدها نظرًا، والله أعلم. ثم الذي لا يشك فيه من تَدَبَّر القرآن أن نساء النبي صلى الله عليه وسلم داخلات في قوله تعالى: {
إِنَّمَا يُرِيدُ اللَّهُ لِيُذْهِبَ عَنْكُمُ الرِّجْسَ أَهْلَ الْبَيْتِ وَيُطَهِّرَكُمْ تَطْهِيرًا }
Book 031, Number 5920:
Yazid b. Hayyan reported, I went along with Husain b. Sabra and 'Umar b. Muslim to Zaid b. Arqam and, as we sat by his side, Husain said to him: Zaid. you have been able to acquire a great virtue that you saw Allah's Messenger (may peace be upon him) listened to his talk, fought by his side in (different) battles, offered prayer behind me. Zaid, you have in fact earned a great virtue. Zaid, narrate to us what you heard from Allah's Messenger (may peace be upon him). He said: I have grown old and have almost spent my age and I have forgotten some of the things which I remembered in connection with Allah's Messenger (may peace be upon him), so accept whatever I narrate to you, and which I do not narrate do not compel me to do that. He then said: One day Allah's Messenger (may peace be upon him) stood up to deliver sermon at a watering place known as Khumm situated between Mecca and Medina. He praised Allah, extolled Him and delivered the sermon and. exhorted (us) and said: Now to our purpose. O people, I am a human being. I am about to receive a messenger (the angel of death) from my Lord and I, in response to Allah's call, (would bid good-bye to you), but I am leaving among you two weighty things: the one being the Book of Allah in which there is right guidance and light, so hold fast to the Book of Allah and adhere to it.
He exhorted (us) (to hold fast) to the Book of Allah and then said: The second are the members of my household I remind you (of your duties) to the members of my family. He (Husain) said to Zaid: Who are the members of his household? Aren't his wives the members of his family? Thereupon he said: His wives are the members of his family (but here) the members of his family are those for whom acceptance of Zakat is forbidden. And he said: Who are they? Thereupon he said: 'Ali and the offspring of 'Ali, 'Aqil and the offspring of 'Aqil and the offspring of Ja'far and the offspring of 'Abbas. Husain said: These are those for whom the acceptance of Zakat is forbidden. Zaid said: Yes.
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