Normality satisfies intermediate subloop condition

From Groupprops

ANALOGY: This is an analogue in algebra loops of a fact encountered in group. The old fact is: normality satisfies intermediate subgroup condition.
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Statement

Suppose $L$ is an algebra loop and $N$ is a normal subloop of $L$ . Then, if $M$ is any subloop of $L$ containing $N$ , $N$ is a normal subloop of $M$ .