Is this a valid join?

Question

(Tablenames changed to protect business secrets).
SELECT MC*
FROM MainCustomers MC,
     ProductsMade       PM,
     OrderLog       OL
WHERE PM.SERIAL_NBR    = OL.SERIAL_NBR
AND Mc.McId          = OL.McID
AND Mc.ProductID = PM.ProductID
 I was asked to translate the above WHERE-based join to the modern TSQL inner join syntax.  At first it sounded easy but then I got confused as to whether it violates proper joining protocol.  For example suppose I wrote the following.
    Select * from t1
    inner join t2 on t1.id = t2.id
    inner join t3 on t3.id = t2.id
    inner join t1 on t1.id = t3.id <---- Huh?
The last line is objectionable because both t1 and t3 were already added to the join in the first few lines so how can we 'join' them again on the last line?
So my question is, isn't the above query making the same mistake? The WHERE clause seems to do the following joins:
PM --> OL
MC---> OL
MC-->PM  (Huh? Re-joined?)
The tables don't  have any sample data right now, maybe I can whip some up shortly.

Answer 1

Ok that's very enlightening. I honestly thought an Inner Join clause was only intended for two tables. Your example is showing three tables
 inner join t3 on t3.id = t2.id  AND  t1.id = t3.id
I had no idea that was appropriate joining protocol. 
yes, you can do that.. I would use it only if it helps to narrow down on the data and get you the data you want.. other wise do not worry on t1.id=t3.id, it would be an unneccssary join..
declare @table1 table (sno int,sname varchar(20))
declare @table2 table (sno int,sname varchar(20),sid1 int)
declare @table3 table (sno int,sname varchar(20))
insert into @table1 values (1,'table1'),(2,'table2'),(3,'table3'),(4,'table4')
insert into @table2 values (1,'table1',1),(2,'table2',2),(2,'table5',5)
insert into @table3 values (1,'table1'),(2,'table2'),(5,'table5'),(3,'table3')
select *
from @table1 A
INNER JOIN @table2 B on A.sno=B.sno
INNER JOIN @table3 C on C.sno=B.sid1 and C.sno=A.sno
select *
from @table1 A
INNER JOIN @table2 B on A.sno=B.sno
INNER JOIN @table3 C on C.sno=B.sid1
Hope it Helps!!
I like this answer the best due to the sample data you provided. Thanks!