Why does the theorem have inclusion if we already have equality

Question

The theorem is as follow:

"Let $G$ be a group and $N$ a subgroup of $G$. TFAE

• The subgroup is normal in $G$
• For all $g$ in $G$, $gNg^{-1}$ is a subgroup of $N$
• For all $g$ in $G$, $gNg^{-1}$ equals $N$

My question: What is the point of #2 if equality already holds in #3.