Does $K \cong K_0$ and $F \cong F_0$ imply $[K : F] = [K_0 : F_0]$?

Question

Let $K$ and $K_0$ be two isomorphic fields and let $F$ and $F_0$ be two isomorphic fields such that $K / F$ and $K_0 / F_0$ are two extensions. I have furthermore that $K_0 / F_0$ is monogenic and his degree is $n \in \mathbb{N}$. Can I state that $[K : F] = n$? Thank you very much in advance.