There is a question about Galois Theory I found:
"Let $L$ be a field and $K$ its prime subfield. Let $\phi$ be an automorphism of $L$. Show that $\phi$ is an automorphism of $L/K$"
All I need is to show that $\phi(a) = a $, $ \forall a\in K$, but I don't know what properties of the prime subfield allows me to prove this.