Is a Composite UNIQUE Constraint On an Already UNIQUE Column Redundant?

I'd just like to clarify something pretty simple regarding single and composite UNIQUE constraints that I can't find a clear answer to. Assume I have the following table:

CREATE TABLE person (
  id INT PRIMARY KEY,
  customer_id INT NOT NULL UNIQUE,
  name VARCHAR(20) NOT NULL
  ...
)

Would it be safe to say that adding the following constraint:

UNIQUE(customer_id, name)

would be redundant and offer no benefit under any circumstance? In other words, is it useless to create a composite UNIQUE constraint that includes a column which is already UNIQUE? This appears to make logical sense, but as I stated, I couldn't find an answer confirming it.