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.

$\blacksquare$