Finite Integral Domain is Galois Field/Proof 4

Proof
$\struct {D, +, \circ}$ is a finite integral domain which is not a field.

From Non-Field Integral Domain has Infinite Number of Ideals, $\struct {D, +, \circ}$ has an infinite number of distinct ideals.

But this contradicts the assertion that $\struct {D, +, \circ}$ is finite.

Hence the result by Proof by Contradiction.