substituting values in column under if-condition SAS

I am fairly new to sas and I am wrapping my head around this problem. I have two tables A and B. The first one collects information about customers in terms of their purchases and the specific products they purchased

A

Customer_id	product_code
1111111	12345
1111111	34523

The second one is some sort of a dictionary, i.e. contains old and new codes, the old code being the key and the new one the updated version.

B

old	new
34523	22256
89765	76576

My goal would be to update in table A, all the references to old codes with their updated (new) version. In the end A should look like

Customer_id	product_code
1111111	12345
1111111	22256

The approach that I wuld take in this example is the following (pseudo-code)

if A.product_code in B.old then
   A.product_code = B.new
else
   nothing

But I am struggling a bit with sas synthax to implement that.

I really hope that my issue is clear enough and do not hesitate to ask further clarification if necessary.

Thanks to anyone who is willing to participate