Need help translating this sentence to predicate logic.
If a student brings a candy bar for him or herself, then that student brings a candy bar for everyone.
Use $C(w)$ as the one-place predicate "$w$ is a candy bar"
Use $B(x, y, z)$ as the three-place predicate "$x$ brings $y$ for $z$"
This is what I have but I am unsure if it's the correct solution $$\exists x(B(x, C(w), x)) \rightarrow \exists x \forall z(B(x, C(w), z))$$