If you have a UNIQUE INDEX then you don’t also need the INDEX – it would be redundant. A UNIQUE INDEX is both a unique constraint and an index that can be used like any other index.
From the documentation:
Note: The preferred way to add a unique constraint to a table is ALTER TABLE … ADD CONSTRAINT. The use of indexes to enforce unique constraints could be considered an implementation detail that should not be accessed directly. One should, however, be aware that there’s no need to manually create indexes on unique columns; doing so would just duplicate the automatically-created index.
Emphasis mine.