Negative of Integer

Theorem
Let $x \in \Z$ be an integer.

Let $x = \eqclass {a, b} {}$ be defined from the formal definition of integers, where $\eqclass {a, b} {}$ is an equivalence class of ordered pairs of natural numbers.

Then:
 * $-x = \eqclass {b, a} {}$

Proof
Follows from Inverses for Integer Addition.