Is every Hadith mentioned in the famous Hadith books, other than the Two Sahihs, to be accepted?

The authors of the Sunan and Musnad collections did not stipulate authenticity for the hadiths they narrated. Their books contained authentic (sahih (definition)), good (hasan (definition)), weak (da'if), and sometimes even fabricated (mawdu') hadiths, because they did not impose the condition of authenticity as did Al-Bukhari and Muslim in their Sahih collections. Therefore, the hadiths in these books cannot be judged as authentic merely because their authors included them; rather, their authenticity must be explicitly stated. Scholars have extracted these hadiths in their books and distinguished their authentic ones from their weak ones.