Polynomial Forms over Field form Integral Domain/Formulation 1/Proof 2

Theorem
Let $\left({F, +, \circ}\right)$ be a field whose zero is $0_F$ and whose unity is $1_F$.

Let $X$ be transcendental in $F$.

Let $F \left[{X}\right]$ be the ring of polynomial forms in $X$ over $F$.

Then $F \left[{X}\right]$ is an integral domain.

Proof
We have from Ring of Polynomial Forms is Commutative Ring with Unity that $F \left[{X}\right]$ is a commutative ring with unity.

The result follows from Ring of Polynomial Forms is Integral Domain.