Confusion about the execution order in SQL query

Confusion about the execution order in SQL query

I'm studying databases with the book "Database System Concepts" from
Silberschatz, Korth and Surdashan (I quote the authors because the
relational algebra notation is different against other authors...
Well, I think that the execution order of a SQL query it's based in the
relational algebra, for example:
If I have this SQL query:
SELECT nombre_sucursal, AVG(saldo) AS media_sucursal
FROM cuenta
GROUP BY nombre_sucursal
HAVING media_sucursal > 800
The corresponding relational algebra expression is the following:
Π nombre_sucursal (σ saldo > 800 (nombre_sucursal Ģ
avg(saldo) (cuenta))
Well... For that, in my opinion, the execution order in a SQL query is (if
you look at the relational algebra expression backwards):
FROM - (cuenta) the base relation in the relational algebra expression
GROUP BY nombre_sucursal - *nombre_sucursal Ģ avg(saldo) in the
relational algebra expression*
HAVING media_sucursal > 800 - σ saldo > 800 the selection operation
in the relational algebra expression
SELECT nombre_sucursal, AVG(saldo) AS media_sucursal - *Π
nombre_sucursal ???*
I put the ??? symbols because this is the part that I don't understand:
If the SELECT clause is the last part of a SQL query, how can I rename the
result of the aggregation function as "media_sucursal" and in the HAVING
clause I'm able to use it?
I checked this question but it confirms what I put above, but not answer
my question.
Any help is welcome!