Unity of Ordered Integral Domain is Strictly Positive

Theorem
Let $\left({D, +, \times}\right)$ be an ordered integral domain whose unity is $1_D$.

Then $P \left({1_D}\right)$, where $P$ is the positivity property.

Proof
We have by definition of the unity that:
 * $\forall a \in D: 1_D \times a = a = a \times 1_D$

This particularly applies to $1_D$ itself: $1_D = 1_D \times 1_D$.

But then by Square of Element of Ordered Integral Domain is Positive $P \left({1_D \times 1_D}\right) \implies P \left({1_D}\right)$.