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 $$\left({\C, + \times}\right)$$.