Rational Numbers form Ordered Integral Domain/Proof 1
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Theorem
The rational numbers $\Q$ form an ordered integral domain under addition and multiplication.
Proof
This follows directly from Rational Numbers form Ordered Field:
The set of rational numbers $\Q$ forms an ordered field under addition and multiplication: $\struct {\Q, +, \times, \le}$.
An ordered field is also an ordered integral domain.
$\blacksquare$