Is 3rd normal form violated in these examples?

Question

Database design

Example No. 1
There is a users table with the following fields:
id (PK), Last name, First name, Middle name, City
Example records:
1, Ivanov, Ivan, Ivanovich, Moscow
2, Petrov, Ivan, Ivanovich, St. Petersburg
3, Sidorov, Ivan , Ivanovich, Moscow The
question is:
Here the City field does not depend on another non-key field, so there are no violations?
I understand that it would be better to put this field in a separate table directory, and put city_id here.

Example No. 2
There is a users table with the following fields:
id (PK), login, Date of birth
Record examples:
1, ivanov, 01/01/2000
2, petrov, 01/01/2001
3, sidorov, 01/01/2002 The
question is the following:
If the login field in the database is not defined unique (not a key), then 3NF is violated because the date of birth depends on the login?

Answer 1

In a relational model, in principle, there can be no dependencies on a non-key.
Which means that the date of birth cannot depend on the login, it depends on the id.
3NF is not violated here, since it simply does not exist here.