Are rinsing the mouth (Mawmaḍah) and inhaling water into the nose (Istinshaq) obligatory during Ghusl for major impurity?

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Rinsing the mouth and inhaling water into the nose are obligatory during Ghusl for major impurity. This is understood to be included in the general instruction given in the Hadith of Umm Salamah, where the command was, "then pour water over yourself," as the mouth and nose are included in what the water covers.