Is it sufficient to perform ghusl for semen that is emitted without desire, without also performing wudu?

The emission of semen without sexual arousal due to an illness does not necessitate ghusl (ritual bath) according to the majority of scholars; rather, it only necessitates wudu (ablution). If one performs ghusl intending it as obligatory, according to those who hold that view, their ghusl is valid even if they do not perform wudu. However, if one imitates the view of the majority and performs ghusl intending it as not obligatory, and does not perform wudu, then their ghusl is not sufficient for the obligatory wudu, because they did not intend to lift the minor ritual impurity from the limbs of wudu.