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The phrase "subordinate principles" is correct and usable in written English.
It can be used in contexts where you are discussing principles that are secondary or lesser in importance compared to primary principles. Example: "In our analysis, we must consider the subordinate principles that support the main theory."
Exact(1)
(Here again, there is a certain obscurity in Reinhold's claim, inasmuch as he insisted that the first principle "determines" only the "form" and not the "content" of all the other, subordinate propositions, yet he also described the relationship between the first principle and the subordinate principles as a "syllogism," in which the latter are "derived" from the former).
Similar(56)
In Celtic poetry, alliteration was from the earliest times an important, but subordinate, principle.
During the half-century of the cold war, the United States undoubtedly subordinated principles as well as causes to the overriding concern of defeating communism.
The Labour leader, Harold Wilson, ever subordinating principle to party, veered from anti-Europeanism to pro-Europeanism to anti-Europeanism and back again.
In the heat of the cold war, they, too, subordinated their moral principles to what they saw as higher purposes.
But he has carefully amassed a wealth of information that suggests Gonzales is less a conservative ideologue than a diligent subordinate whose only principle is abject fealty to Bush.
Cammack (2004: 190) affirms that while the World Bank is committed to poverty alleviation, its intentions and development programs are subordinated to capitalist principles.
A cost-effectiveness principle that concerns choices between different interventions for the individual patient must be applied as proposed by the inquiry, and is subordinated to the principles of human dignity and needs and solitary.
In Bentham's hands this took the form of a multitude of subordinate or secondary ends, principles and maxims designed to give practical direction to the utility principle in each and every aspect of the law.
Amazingly, Lee creates such a work of art, not by tamping down his style, suppressing his personal impulses, or subordinating his intuitions to principles, but by heightening and extending his style.
Randazza's letter concluded: "I am certain that neither party wishes to see First Amendment rights subordinated to international trademark principles, thus unwittingly proving Mr. Beck's point.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com