Regarding the term

The questioner : Our Shaykh, regarding the fifth classification, "hasan sahih," since it is sahih, do we need the hasan? That is, is it currently arranged...?

The Shaykh : No, you must know how it reached the status of sahih. Did it reach the status of sahih through the aggregate of five weak chains, or did it reach the status of sahih through the aggregate of a chain that is hasan in itself, plus other weak chains that strengthened it? Do you see the difference?

The questioner: Yes.

The Shaykh : That is, if the weakness is in all the chains, it becomes sahih li-ghayrihi (sahih due to other chains). If the weakness is not in all the chains but in the majority of them, and one of them is hasan in itself, the important thing is that the expression be concise and clear. So, if we say "a hadith is sahih" and we define it in terminology as "sahih due to the aggregate of its weak chains," and if we say "hasan sahih," it is sahih due to the aggregate of a chain that is hasan in itself, plus chains that support it...
The student : The hadith of the prayer of tasbih (prayer of glorification); one of its chains is hasan, and it has many other chains, so it becomes hasan sahih.