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.
$\blacksquare$