electromagnetism - Proof that four-vector potential is a valid four vector

The definition of $ A^{\mu}$ that I've been given is as an object created from the scalar field $\phi$ and the vector field $\vec{A}$ i.e:

$$ A^{\mu} = (\phi,\frac{\vec{A}}{c}) $$ [in cgs units]

How do I formally prove that this is in fact a valid four vector, and not some jumble of objects?

(The Proof that four-potential is a four-vector question does not answer this - it posits some strange specific case.)