All Musnad Hadith in Bukhari and Muslim are Sahih.
The vast Majority of Ahl al-Sunnah scholars are in agreement that all the Hadith in Bukhari and Muslim, which have complete chains of narration (Musnad), are authentic (Sahih). This does not include the Mu’alaqaat or Balaghaat in these books, because they have not been narrated with complete chains. However, there are very few such narrations in Bukhari and Muslim.
جَمِيع مَا حكم مُسلم بِصِحَّتِهِ من هَذَا الْكتاب فَهُوَ مَقْطُوع بِصِحَّتِهِ وَالْعلم النظري حَاصِل بِصِحَّتِهِ فِي نفس الْأَمر وَهَكَذَا مَا حكم البُخَارِيّ بِصِحَّتِهِ فِي كِتَابه وَذَلِكَ لِأَن الْأمة تلقت ذَلِك بِالْقبُولِ سوى من لَا يعْتد بِخِلَافِهِ ووفاقه فِي الْإِجْمَاع (صيانة صحيح مسلم)
Everything that (Imam) Muslim considered to be Sahih of this book is undoubtedly Sahih, and it leads to contemplative certainty due to its authenticity. Likewise, everything that (Imam) al-Bukhari considered to be Sahih in his book (is Sahih), because the Ummah has accepted that reality (the authenticity of Bukhari and Muslim) with agreement. With the exception of a few, whose acceptance or disagreement does not affect the consensus. (Imam Ibn Salah, Siyanatu Sahih Muslim).
وأجمعت الأمة على صحة هذين الكتابين، ووجوب العمل بأحاديثهما (تهذيب الأسماء واللغات)
The Ummah is unanimously agreed that these two books are Sahih, and that their Hadith narrations must be acted upon. (Imam al-Nawawi, Tadheeb al-Ismaa wa al-Lughaat).
أَبَا الْمَعَالِي عبد الْملك بن عبد الله بن يُوسُف الْجُوَيْنِيّ بنيسابور يَقُول لَو حلف إِنْسَان بِطَلَاق امْرَأَته أَن مَا فِي كتابي البُخَارِيّ وَمُسلم مِمَّا حكما بِصِحَّتِهِ من قَول النَّبِي صلى الله عَلَيْهِ وَسلم لما ألزمته الطَّلَاق وَلَا حنثته لإِجْمَاع عُلَمَاء الْمُسلمين على صحتهما (صيانة صحيح مسلم)
Abu al-Ma’aali al-Juwayni said, if a man took an oath to divorce his wife based on the fact that everything Bukhari and Muslim said is Sahih in their books regarding the words of the Prophet ﷺ, then divorce is not binding upon him. Nor has he broken his oath, due to the consensus of Muslim scholars that they (the Hadith narrations) are Sahih. (Siyanatu Sahih Muslim).
These are just some references from classical, authoritative books proving that all Musnad Hadith in Sahih al-Bukhari and Sahih Muslim are Sahih.
There is a lot of misinformation and misguidance being spread regarding the blessed Hadith of the Holy Prophet ﷺ. Thus, it is very important for Muslims to study the science of Hadith (Mustalah al-Hadith) with reliable teachers.
– Answered by Shaykh Noorud-deen (05.01.2021)
Are weak Hadith always rejected?