Is the ablution of one who intended to perform ablution (wudu'), then took a ritual bath (ghusl) without performing wudu', valid?

If the ghusl (definition) is not obligatory (such as ghusl for Eid or for cooling down), then it does not suffice for wudu' unless one has the intention of wudu'. The person performing ghusl must be careful not to touch his private parts, and to observe the order of the wudu' limbs according to those who deem it obligatory. However, if the ghusl is obligatory (such as ghusl from janabah (definition) or menstruation), then it suffices for wudu', because the intention to remove the major ritual impurity is sufficient for the minor one, and this is an agreed-upon opinion.