We were given a proof in class that is as follows:
Given a finite extension $E/F$ the following are equivalent
1) $E/F$ is normal
2) If $\alpha \in E$ then the minimum polynomial of $\alpha$ over $F$ splits over $E$
3) If $L/E$ and $\sigma \in {\rm Gal}(E/F)$ then $\sigma(E)=E$
4) $E$ is a splitting field for some $m \in F[x]$
I understand 1,2 and 4 but I don't understand 3.
I am really confused by the L as it seems to play no role in the second half of the sentence(I think maybe there's some typo here).
Could anyone please tell me the correct statement/ explain its meaningfulness, please?