If $H$ is Lie subgroup embedded in a Lie group $G$, then $H$ is closed

Question

I read the demonstration that if $G$ be a Lie group and $H \subset G$ a closed subgroup of $G$. Then $H$ is an embedded Lie subgroup of $G$. The author mentions that the reciprocal is true, but does not prove it. I am trying to demonstrate this, but I am unable to devise a strategy. Could you give me a hint?