Proof of Theorem CFDVS

Since $V$ has dimension $n$ we can find a basis of $V$ of size $n$ (Definition D) which we will call $B$. The linear transformation $\vectrepname{B}$ is an invertible linear transformation from $V$ to $\complex{n}$, so by Definition IVS, we have that $V$ and $\complex{n}$ are isomorphic.