Integers form Ordered Integral Domain/Proof 2

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Theorem

The integers $\Z$ form an ordered integral domain under addition and multiplication.


Proof

From Integers form Integral Domain we have that $\struct {\Z, +, \times}$ forms an integral domain.

From Integers form Totally Ordered Ring, $\struct {\Z, +, \times}$ is a totally ordered ring.

Hence the result.

$\blacksquare$