Does Unit Tests still matter if Functional Tests is satisfied?

For a short summary:

• Unit tests are the smaller ones that expects something to do it right in dev's view.
• Functional tests are those that expects things are right in user's view

If Functional Tests are already satisfied, do we still need to do Unit Tests?

Most likely (let's use web development as context), this is common by using the browser to see if things are right by letting other users/people try the system/application.

Let us put out other tests like for edge cases.