I think that is the vital point to live. After this, white has a couple of choices.
If white tries to break out with , black can simply kill them with
and
.
If white tries , black plays this way, and ends with a live shape.
And finally, White is too short on liberties to be able to play . After
, white's stones are again dead.
If here, then
kills. Black cannot play at a due to shortage of liberties.