Is the rinsing of the mouth and nose that accompanies the ablution sufficient for the ritual bath for major ritual impurity?

Question:
He says: Honorable Shaykh, may Allah grant you success. He says: If a person is in a state of major ritual impurity, and when he intends to take the ritual bath, he performs the ablution for prayer, and then pours water over his entire body, is it obligatory for him to rinse his mouth and nose during the ritual bath, or is what he did with the ablution sufficient?

Answer:
What was done with the ablution is sufficient, because the ablution is a prerequisite for the ritual bath, so the rinsing of the mouth and nose with the ablution is sufficient. Yes.