Using DISTINCT inner join in SQL

I have three tables, A, B, C, where A is many to one B, and B is many to one C. I'd like a list of all C's in A.

My tables are something like this: A[id, valueA, lookupB], B[id, valueB, lookupC], C[id, valueC]. I've written a query with two nested SELECTs, but I'm wondering if it's possible to do INNER JOIN with DISTINCT somehow.

SELECT valueC
FROM C
INNER JOIN
(
    SELECT DISTINCT lookupC
    FROM B INNER JOIN
    (
        SELECT DISTINCT lookupB
        FROM A
    ) 
    A2 ON B.id = A2.lookupB
) 
B2 ON C.id = B2.lookupC

EDIT: The tables are fairly large, A is 500k rows, B is 10k rows and C is 100 rows, so there are a lot of uneccesary info if I do a basic inner join and use DISTINCT in the end, like this:

SELECT DISTINCT valueC
FROM 
C INNER JOIN B on C.id = B.lookupB
INNER JOIN A on B.id = A.lookupB

This is very, very slow (magnitudes times slower than the nested SELECT I do above.