Divisor Relation is Transitive/Proof 1

Theorem

The divisibility relation is a transitive relation on $\Z$, the set of integers.

That is:

$\forall x, y, z \in \Z: x \divides y \land y \divides z \implies x \divides z$

Proof

We have that Integers form Integral Domain.

The result then follows directly from Divisor Relation in Integral Domain is Transitive.

$\blacksquare$