I am not sure this question is proper for this site, but there is no other places that I can get an answer. So if anyone can give an answer for this, it would be very helpful to me.

Let $F$ be a finite extension of $\mathbb{Q}_\ell$. Let $F_1$ is a finite Galois extension of $F$ and $F_\infty$ is a Galois extension of $F$ which is also an extension of $F_1$. Suppose we know $\mathrm{Gal}(F_\infty/F_1)\cong \mathbb{Z}_p$ or $\mathbb{Z}_p\times \mathbb{Z}_p$ for some $p\neq \ell$. With these assumption, why the extension $F_\infty/F_1$ should be unramified? The only information I know is the result comes from class field theory, but I cannot catch it.