When studying normal closures, I came across the following in the proof for the existence of normal closures for finite extensions:
If $K \overset{i}\rightarrow L$ is finite, $g \in K[X]$ and $L \overset{j}\rightarrow F$ is a splitting field extension for $i(g) \in L[X]$, then $K \overset{j \circ i}\rightarrow F$ is a splitting field extension for $g$.
Could anyone please direct me to a proof for this or be kind enough to explain why this is true?