[SQL] Addresses stored in a database should you normalize?

quick question.

consider the following table (UK):

• CustomerID (PK)
• First Name
• Surname
• House_No/name
• street
• City
• Postcode

Would you split off address into another table? basic business assumption is that a customer cannot have more than one address.

originally i seperated this off to look something like this:

Customer Table

• CustomerID (PK)
• FirstName
• Surname
• AddressID (FK)

Address Table

• AddressID(PK)
• Postcode(FK)
• House_Number_name

Postcode Table:

• Postcode (PK)
• StreetName
• CityID(FK)

City Table

• CityID (PK)
• CityName

unless i have my assumptions wrong that a postcode uniquely identifies a streetname and city is this not in 3NF?

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