Prove each of the following statements using a direct proof, a proof by contrapositive, a proof by contradiction, or a proof by cases

For any three integers x, y, and z, if y is divisible by x and z is divisible by y, then z is divisible by x.

Defintion of divisible:

An integer n is divisible by an integer d with d 0, denoted d | n, if and only if there exists an integer k such that n=dk.