Unity Divides All Elements

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

Then unity is a divisor of every element of $D$:


 * $\forall x \in D: 1_D \backslash x$

Proof 1
The element $1_D$ is the unity of $\left({D, +, \circ}\right)$, and so:
 * $1_D \in D: x = 1_D \circ x$

The result follows from the definition of divisor.

Proof 2
This is a special case of Every Unit Divides Every Element, as Unity is a Unit.