How Do You Write An UPDATE Store Procedure?

I have these 3 tables that are related to each other. I am trying to change the brand name of a product and the type of the product. How can I do this?
 1 CREATE TABLE Products
2 (
3 ProductID int IDENTITY (1,1) PRIMARY KEY,
4 ProductSKU nvarchar(100) NOT NULL UNIQUE,
5 ProductName nvarchar(255),
6 ProductDescription nvarchar(MAX),
7 isInStock bit,
8 SalePrice decimal (18,2),
9 UnitPrice decimal (18,2),
10 isOnSale bit,
11 isSpecial bit,
12 isActive bit,
13 ProductRating int,
14 ProductImageBig varchar(255),
15 ProductImageMedium varchar(255),
16 ProductImageSmall varchar(255)
17 );
18
19 CREATE TABLE Brands
20 (
21 BrandID int IDENTITY (1,1) PRIMARY KEY,
22 BrandName nvarchar(255) NOT NULL UNIQUE
23 );
24
25 CREATE TABLE Types
26 (
27 TypeID int IDENTITY (1,1) PRIMARY KEY,
28 TypeName nvarchar(150) NOT NULL UNIQUE
29 );
30
31 // The store procedure I am having trouble with.
32
33 CREATE PROC SetProductsSKU_Brand_Type
34 @ProductID int,
35 @BrandName nvarchar(255),
36 @TypeName nvarchar(150),
37 @ProductSKU nvarchar(100),
38 @ProductName nvarchar(255),
39 @isInStock bit,
40 @SalePrice decimal (18,2),
41 @UnitPrice decimal (18,2),
42 @isOnSale bit,
43 @isSpecial bit,
44 @isActive bit
45 AS
46 UPDATE Products, Types, Brands
47 SET [BrandName] = @BrandName, [TypeName] = @TypeName, [ProductSKU] = @ProductSKU, [ProductName] = @ProductName, [isInStock] = @isInStock,
48 [UnitPrice] = @UnitPrice, [isSpecial] = @isSpecial, [isActive] = @isActive
49 FROM Products prod INNER JOIN ProductsBrands pb
50 ON prod.ProductID = pb.ProductID INNER JOIN Brands b
51 ON pb.BrandID = b.BrandID INNER JOIN ProductsTypes tp
52 ON prod.ProductID = tp.ProductID INNER JOIN Types t
53 ON tp.TypeID = t.TypeID
54 WHERE prod.ProductID = @ProductID
55 AND [ProductSKU] = @ProductSKU
56 AND [ProductName] = @ProductName
57 AND [isInStock] = @isInStock
58 AND [UnitPrice] = @UnitPrice
59 AND [isSpecial] = @isSpecial
60 AND [isActive] = @isActive
61 AND b.BrandName = @BrandName
62 AND t.TypeName = @TypeName