Degree of Product of Polynomials over Ring/Corollary 2

Theorem
Let $\left({D, +, \circ}\right)$ be an integral domain whose zero is $0_D$.

Let $D \left[{X}\right]$ be the ring of polynomials over $D$ in the indeterminate $X$.

For $f \in D \left[{X}\right]$ let $\deg \left({f}\right)$ be the degree of $f$.

Then:
 * $\forall f, g \in R \left[{X}\right]: \deg \left({f g}\right) = \deg \left({f}\right) + \deg \left({g}\right)$

Proof
An integral domain is a commutative and unitary ring with no proper zero divisors.

The result follows from Degree of Product of Polynomials over Ring: Corollary 1.