The phrase "without reliance on" is correct and usable in written English.
You can use this phrase to describe a situation where someone does not need to rely on any particular person, thing, or information to complete a task. For example, "He was able to complete the project without reliance on any outside sources."
Yet, the offering memorandum for Class V Funding III stated that the Credit Suisse unit was not acting as "advisors" or "agents" to the buyer, and that any buyer should make its investment decision determine "without reliance" on either.
Milius professed ambivalence to fantasy elements, preferring a story that showcases accomplishments realized through one's own efforts without reliance on the supernatural.
Thus it appears that, from Plato's point of view, D3 establishes, without reliance on Purity-F or any other potentially problematic assumption, that if the one is, then the others have a host of contrary properties.
Thus it appears that, from Plato's point of view, D5 establishes, without reliance on Purity-F or any other potentially problematic assumption, that if the one is not, then the one has a host of contrary properties.
Thus it appears that, from Plato's point of view, D8 establishes, without reliance on Purity-F or any other potentially problematic assumption, that if the one is not, then the others are, at the very least, neither one nor many.
Thus it appears that, from Plato's point of view, D6 establishes, without reliance on Purity-F or any other potentially problematic assumption, that if the one is not, then the one has neither of a host of contrary properties.
Thus it appears that, from Plato's point of view, D7 establishes, without reliance on Purity-F or any other potentially problematic assumption, that if the one is not, then the others appear to have a host of contrary properties.
Truth, as he saw it, could be discovered only by abstract reasoning, without reliance on sense perception or observation of outside phenomena.
Good solar generation, for example, especially combined with high-efficiency LED lighting, allows for extended camping trips without reliance on a generator.
After about a decade of trial and error in some cases, chicken companies are showing that raising animals without reliance on antibiotics is not only possible, it's profitable.
While one can agree that such sources shouldn't be used except when necessary, you acknowledge that some of the most important articles simply couldn't be written without reliance on sources who will not agree to speak on the record.
