Given the subgroups $H$ and $N$ normal of group $G$, what is ${\rm Im}(\phi)$ regarding $\phi:H\to G/N$

Question

Given the subgroups $H$ and $N$ normal of group $G$ and let $\phi: H \rightarrow G/N$ defined as $\phi(h)=hN$ (standard canonical group homomorphism by $\phi: G \rightarrow G/N$), then the ${\rm Im}(\phi)$ should be ${\rm Im}(\phi) = HN/N$ by my old lecture notes, but I am looking at this for 10 minutes now and I can't see (anymore) why this should be true