Subset Products of Normal Subgroup with Normal Subgroup of Subgroup

Theorem
Let $G$ be a group.

Let:
 * $(1): \quad H$ be a subgroup of $G$
 * $(2): \quad K$ be a normal subgroup of $H$
 * $(3): \quad N$ be a normal subgroup of $G$

Then:
 * $N K \triangleleft N H$

where:
 * $N K$ and $N H$ denote subset product
 * $\lhd$ denotes the relation of being a normal subgroup.