In the above picture, there is a sentence as follows:
If $x\in B$ is an integral element of $L$, then all of its conjugates $\sigma x$ are also integral.
If $x\in B$, then all of its conjugates $\sigma x$ are also integral (over $A$). Thus it is not necessary to say $x$ is an integral element of $L$, it suffices to state it as follows:
If $x\in B$, then all of its conjugates $\sigma x$ are also integral.
Is my viewpoint correct?