Reference: I’laam al-Mu’aasireen bi-Fataawa Ibn ‘Uthaymeen – Page 40
Question: If a person enters the state of janaabah (major sexual impurity), and then took a bath, is he required to perform the ablution after having taken a bath?
Response: If a person was in a state of janaabah and then took a bath, then his bathing suffices (and he is not required to perform) the ablution even if he had not made the intention, as He (Subhaanahu wa Ta’aala) says:
However, take note that it is imperative gargling and sniffing water up the nose and blowing it out [both as done in the ablution] is done during the bath for janaabah.