Weil group of non archimedian field

Question

Let $F$ be a finite extension of $\Bbb{Q}_p$. Let $W_F$ be the Weil group of $F$. Let $I_F$ be the inertia group of $F$. Let $\phi$ be an element of the weil group of $F$ which does not belong to the inertia subgroup. Then how to show that there exists a finite extension $E$ of $F$ such that $W_E$ is the group $<\phi, I_E>$ generated by $\phi$ and $I_E$ and $W_E$ is an open subgroup of $W_F$ of finite index.