I think I might have noted some paralels:
There is one more piece to this picture.
We anglophones learn that du, de la, de l' and often des all become de or d' in the negative.
eg.
J'ai du vin --> Je n'ai pas de vin. / I have some wine --> I don't have any wine.
J'ai de l'eau --> Je n'ai pas d'eau.
J'ai de la bière --> Je n'ai pas de bière.
The partitive in the informative sentences would be likely to be translated as
some (although, in many cases it is omitted). Whereas in negative sentences when it becomes
de it is translated as
any (see also below)
.
What our instructors usually forget to tell us is that this rule
does not apply when you are identifying something with the verb
être:
eg.
C'est du vin --> Ce n'est pas du vin. / It is (some) wine. --> It is not wine.
C'est de l'eau --> Ce n'est pas de l'eau.
C'est de la bière --> Ce n'est pas de la bière.
Remember that
ni is a negation... so the sentence says "It's not water, nor wine, but beer." Clearly, we are using être to identify this substance, so we cannot replace the partitive with
de.
Ce n'est pas d'eau, ni de vin, mais de la bière.
Ce n'est pas de l'eau, ni du vin, mais de la bière. 
[...]
geostan said:
The reduction of a partitive after a negative does not apply to the verb etre because it is not a question of absence, but of identification. When one says:
Je n'ai pas d'argent. We show an absence of money.
But when we say Ce n'est pas de l'eau, there is no absence; there is something there; it's simply not water.
The rule is that the partitive article doesn't become de in the construction C'est/Ce sont. I see another parallel:
C'est de la bière --> Ce n'est pas de la bière.
This is beer. --> This is not beer.
Ce sont des pommes de terre. --> Ce ne sont pas des pommes de terre.
These are potatos. --> These aren't potatos.
So, here we have the partitive article in both French sentences and its equivalent in the English ones, that's to say its absence.
du/de la/d'/des = ø (very often, but not always).
Using
être to point out the absence of something we need another construciton, for instance:
Il n'y a pas de
Il y a du vin. There's (some) wine.
but
Il n'y a pas de vin. There's no wine.
I hope I didn't make any mistake in what I've just written.
Tom