First of all, you should stop using deprecated implicit joins and use explicit joins instead. Then you can use table aliases for this:
WITH subselect_from_A AS (
SELECT A.A_ID FROM A --doesn't really seem like a sub-select
)
SELECT B.D_ID, A.A_ID
FROM B
INNER JOIN subselect_from_A AS A
ON B.B_ID = A.A_ID;