Does a regular ghusl suffice for wudu for prayer?

It is recommended to perform ablution (wudu) before ghusl (ritual bath). If the ghusl is performed to remove a major ritual impurity (hadath akbar), such as from seminal emission (janabah) or menstruation (hayd), and the person performing ghusl thoroughly washes their entire body with water, along with rinsing the mouth and nose, then this ghusl suffices for ablution, and ablution is not obligatory afterward. However, a ghusl performed for cooling down or for cleanliness does not suffice for ablution, because it is not an act of worship.