Group homomorphism/Preimage of normal subgroups/Normal subgroup/Exercise

Let ${}G$ and ${}H$ be groups, and let

$\varphi \colon G\longrightarrow H$

be a group homomorphism. Show that the preimage ${}\varphi ^{-1}(N)$ of a normal subgroup ${}N\subseteq H$ is a normal subgroup in ${}G$.

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