Is the intention to remove major ritual impurity obligatory in the full ritual bath?

Question:
He says: I contracted major ritual impurity before I went to sleep, so I intended to get up before dawn and perform the full ritual bath. I woke up before the dawn prayer and performed the full ritual bath while forgetting that I was in a state of major ritual impurity. Then, during the prayer, I remembered that I had not renewed the intention. Is my action valid, and what is the ruling on my prayer?

Answer:
Yes, if you performed the full ritual bath for cleanliness or to cool off at dawn and did not intend to remove the major ritual impurity, then the major ritual impurity remains upon you and your prayer is not valid. You must perform the full ritual bath to remove the major ritual impurity with the intention, for indeed deeds are by intentions, and every person will have what he intended. You perform the full ritual bath with the intention of removing the state of ritual impurity and the major ritual impurity, and you repeat the prayer you performed.