Joining same table on itself

Joining same table on itself

One of my table stores the UserAgent from the user's browser along with
the corresponding UID associated with it, with some other data. This
occurs every time a user logs in. So they will have many entries per user.
I am trying to query this table to find some unique users based on
qualities.
For example, I am trying to find only users that have used IE6 and no
other browsers. The closest I can get so far is through this method:
select distinct (U.UID) from TABLE1 tb1
inner join TABLE1 tb2 on tb1.UID = tb2.UID
where tb1.UserAgent like '%MSIE 6.%'
and tb2.UserAgent like '%MSIE 6.%'
This seems to return users whom have used IE6 and any other browser as
well. I am trying to find basically the opposite of this. Users that have
used IE6 and IE6 only. I also tried the one below but didn't quite work
either because a good chunk of this users had other entries with non IE6
browsers.
select distinct (U.UID) from TABLE1 tb1
inner join TABLE1 tb2 on tb1.UID = tb2.UID
where tb1.UserAgent like '%MSIE 6.%'
and tb2.UserAgent not like '%MSIE 6.%'
I think I am on the right track but could be way off here.
TIA!