Nested Exists Query

I am trying to write a query that does not use inner joins to see if it returns rows faster than a query using inner joins.
My trouble is that I don't know how to write the syntax for the 3rd table that I am comparing against.
Can I nest Exists in a Where clause?
If so how is the 2nd exists statement added to the query?
see my sample query below
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'With 2 tables

SELECT DISTINCT s1.ID, s1.SITE
FROM SITE_TBL s1
WHERE EXISTS (SELECT *
FROM DEVICE_TBL d1
WHERE s1.ID = d1.SITE_ID AND d1.DELETEFLAG <> 'D')
ORDER BY SITE



'with 3 tables this doesn't work

SELECT DISTINCT s1.ID, s1.SITE
FROM SITE_TBL s1
WHERE EXISTS (SELECT *
FROM DEVICE_TBL d1
WHERE s1.ID = d1.SITE_ID AND d1.DELETEFLAG <> 'D')
AND
(SELECT *
FROM BIG_TBL b1
WHERE d1.fqdn = b1.xyz)
ORDER BY SITE

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Thanks for the help
Jim