set not null column using existing constraint

Looking at the postgres documentation (https://www.postgresql.org/docs/9.6/static/sql-altertable.html):

"If PRIMARY KEY is specified, and the index's columns are not already marked NOT NULL, then this command will attempt to do ALTER COLUMN SET NOT NULL against each such column. That requires a full table scan to verify the column(s) contain no nulls. In all other cases, this is a fast operation."