Help With Nested Query

I am having trouble with the following query.

Important Tables:
Product (table of products)
--ProductID
--ProductName

ProductCategories (Associates a Product with one or more categories)
--ProductID
--CategoryID

Category (table of categories that a product may fall under)
--CategoryID
--CategoryName

Information:

Basically I have a product that falls into two categories. Therefore there are two records in the ProcuctCategories Table. I am trying to create a query that will find all products that are in categories 1 & 2.

Attempted Solution:
SELECT * FROM Product
WHERE (ProductID IN (SELECT CategoryID FROM ProductCategories WHERE CategoryID =1))
AND
(ProductID IN (SELECT CategoryID FROM ProductCategories WHERE CategoryID =2))

This returned zero records though it should have returned the product that is in categories 1&2.

I would appreciate any help available.

Thank you,
-Patrick