If $\displaystyle \sigma_{1}, \sigma_2, \ldots, \sigma_{n} $ is a group of automorphisms of a field $\displaystyle E $ and if $\displaystyle F $ is a fixed field of $\displaystyle \sigma_{1}, \sigma_{2}, \ldots, \sigma_{n}, $ then $\displaystyle (E/F) = n $.

How would I prove this?