The phrase "depend not on" is grammatically correct and can be used in written English, although it may sound more formal or poetic than everyday language.
It is often used to convey a strong or emphatic statement. Example: The success of this project will depend not on individual efforts, but on the collaboration of the entire team.
Such a feat will depend not on the will of one individual, but upon one (or more) government's willingness to foot the tab.
It will not be the same as the first one, since it will depend not on a few miracle varieties but on tailoring existing seeds to different environments.
The survival of our species in the New Millennium will depend, not on ancient conflicts, but on new ways of dealing with one other in spite of different gods and different mores.
However, if one questions this assumption, in the way that is necessary when the purpose of enquiry is to find out whether animals are conscious, its justification turns out to depend, not on careful functional analysis of visual perception, but on reasoning by analogy from one's own case (Heyes 2008).
The experiment's turbulent winds, however, depend not on Mother Nature, nor massive Hollywood special-effects fans.
We can build new systems of human relations which depend not on secrecy but on connectivity.
Large swathes of China, particularly in the north, depend not on rice, but on wheat.
One of the arts of diplomacy is to find solutions to problems that depend not on trust but on interest.
Regardless of our orientation, we depend not on their tolerance, but on their approval, their acceptance and encouragement.
This will ultimately depend not on what we do as Americans but on whether he listens to or ignores our growing discord.
But the best bet is that the outcome on Tuesday will depend not on the latest news but on each side's success in getting their supporters to vote.
