Rational Numbers form Subfield of Complex Numbers

Theorem
Let $\left({\Q, +, \times}\right)$ be the Field of Rational Numbers.

Let $\left({\C, +, \times}\right)$ be the Field of Complex Numbers.

Then $\left({\Q, +, \times}\right)$ is a subfield of $\left({\C, +, \times}\right)$.

Proof
From Rationals form a Subfield of Reals, $\left({\Q, +, \times}\right)$ is a subfield of $\left({\R, + \times}\right)$.

From Real Numbers form Subfield of Complex, $\left({\R, +, \times}\right)$ is a subfield of $\left({\C, + \times}\right)$.

Thus from Subfields Transitive $\left({\Q, +, \times}\right)$ is a subfield of $\left({\C, + \times}\right)$.