A tree edge $uv$ with $u$ as $v$’s parent is a cut edge if and only if there are no edges in $v$’s subtree that goes to $u$ or higher

Referring to these notes regarding DFS – Click Here

They refer to the following claim as observation:

A tree edge $ uv$ with $ u$ as $ v$ ’s parent is a cut edge if and only if there are no edges in $ v$ ’s subtree that goes to $ u$ or higher.

However, I don’t really understand why is that obvious or how can it be proved.

I’d appreciate a proof of this claim.