Is 〜でなかった valid?


I have from the entry for 実際 of ウィズダム英和・和英辞書 the following sentence:

> 彼は医者だと言ったが実際はそうでなかった。
>
> He said he was a doctor, but in fact he was not.

From what I understand, the 「〜でなかった」 here is supposed to be the past negative
form of 「〜である」. However, isn't the negative form of 「〜である」「〜で **は** ない」?
Shouldn't that sentence have ended with 「で **は** なかった」instead?




This research
<https://www.lang.nagoya-u.ac.jp/nichigen/menu7_folder/symposium/pdf/11/07.pdf>
explains

”でない”は is most often used in non-past conditional 仮定条件形, then it goes as the
following order , the attributive form 連体形, the parataxis form 並立形, and the
conclusive form 終止形.

ex:) 弁護士試験は、優秀でないと合格できない。

If you are not clever, you can't pass the bar examination.

On the other hand "ではない” is used by nearly 60% in the conclusive form 終止形,
then it goes as the following order, the parataxis form 並立形, past conditional.

ex:) 佐々木さんは、歯医者さんではない。

Mr.sasaki is not a dentist.

Hope it helps.

