Is the following argument "Let $H$ be Lie group and an open subgroup of $G$ a Lie group, then $H$ is closed" true?

Question

In my notes of Lie algebra I have the following statement, which is unproven and has no further clarification:

Let $H$ be Lie group and an open subgroup of $G$ a Lie group, then $H$ is closed

Is this true or is it a mistake? and if it is, how is it proven?