# Negative in Integral Domain is Unique

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## Theorem

Let $\struct {D, +, \times}$ be an integral domain.

Let $a \in R$.

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

## Proof

From the definition of an integral domain, $\struct {D, +, \times}$ is a ring.

The result follows from Ring Negative is Unique.

$\blacksquare$