Negative of Element in Field is Unique/Proof 1

Theorem

Let $\struct {F, +, \times}$ be a field.

Let $a \in F$.

Then the negative $-a$ of $a$ is unique.

Proof

By definition, a field is a ring whose ring product less zero is an abelian group.

The result follows from Ring Negative is Unique.

$\blacksquare$