Monomorphism from Rational Numbers to Totally Ordered Field

Theorem
Let $$\left({F, +, \circ; \le}\right)$$ be a totally ordered field.

There is one and only one (ring) monomorphism from the totally ordered field $$\Q$$ onto $$F$$.

Its range is the prime subfield of $$F$$.

Proof
Follows from Characteristic of Totally Ordered Integral Domain and Quotient Field Order Monomorphism Unique.