COUNT the # of DISTINCT IDs, but only when multiple records exist in a table

Let's say I have开发者_StackOverflow中文版 the following MySQL table:

id  tagid  campaignid
1   10     1000
2   11     1000 
3   12     1000
4   13     1000
5   12     2000
6   13     2000
7   12     3000
7   12     4000

I need to COUNT the number of DISTINCT campaignids, but only when records exist for multiple tagids.

For example, count the number of unique campaignids when a record exists for all of the following tagids - 10, 11 & 12. In this case, the result would be a count of 1 (only campaignid 1000 has a record for all of these tagids)

Another example, count the number of unique campaignid when a record exists for both tagid 12 & 13. In this case, the result would be a count of 2 (campaignid 1000 & 2000 both have a record for both of these tagids). campaignid 3000 & 4000 have a record for tagid 12, but not a record for tagid 13, so they are not included.

Any thoughts on the SQL statement I could use to accomplish this?

Many thanks.

A somewhat simplified version of Jack Maney's answer using Having

 SELECT Count(campaignid)
   FROM
    (SELECT  campaignid 
     FROM  table
     HAVING   count(tagid) > 1
     GROUP BY campaignid ) t

Assuming you're interested in the occurrence of a specific list of tagIDs perhaps something like the following: (Disclaimer: I use Sql Server)

select count(campaignid)
from (
  select campaignid
  from table
  where tagid in (12, 13)        --change the list of tagids as desired
  group by campaignid
  having count(distinct tagid)=2 --this count should be the exact size of the tagid list above
  ) t

Just count the campaignid's for each (id,tagid) pair, only take the rows where this count is at least 2, and then do a final tally:

select count(1) from
(
  select campaignid from
    (
    select id, tagid, count(campaignid) as freq
    from table
    group by id, tagid
    )
  join table using (id,tagid)
  where freq>=2
  group by campaignid
)