The first observation to make is that threatens to connect outside with . After , Black may not play at a due to shortage of liberties.
is the key to prevent the aforementioned ko. Although and can capture the Black corner, and is a standard tesuji to destroy the outside eye. As it turns out, the corner becomes a flower six dead shape after .
It is sufficient to connect at . If denies the connection, then captures the corner. When prevents White from making the outside eye, to starts a ko. It is almost impossible for Black to win this ko. (If at , then White can make an eye at a for unconditional life.)