[Newbie] UPDATE based on other table content

Hello.

I have a very basic question, relative to the following "problem".

I have the following tables:

product
    id
    qty

intermediate
    id
    product_id

orders
    intermediate_id

I want to update the "qty" field of the "product" table by incrementing
it each time there is an order in the "orders" table, referencing a
given product through the "intermediate" table.

I tried the following request:

UPDATE
        qty = qty+1
FROM
    intermediate,
    orders
WHERE
    orders.intermediate_id=intermediate.id AND
    intermediate.product_id=product.id
;

But of course it does what was predictable - ie the qty "field" is
incremented only once, even if more than one entry is referencing a
given product. But it's not what I was hoping...

What would be the "good" solution to do that UPDATE?

Thanks for your attention!
Daniel Chiaramello