بَدَلُ الْكُلِّ مِنَ الْكُلِّ: وَهُوَ مَا مَدْلُولُهُ مَدْلُولُ الْمَتْبُوعِ، نَحْوُ: «جَاءَنِي زَيْدٌ أَخُوكَ».
Translation: Whole-for-whole badal denotes the very same referent as its antecedent, as in: Zayd, your brother, came to me.
Zayd and your brother point to one person. "Whole" does not mean an entire population; it means coextensive reference here.