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The phrase "a cardinal principle" is correct and usable in written English.
This phrase is typically used to describe an important guiding principle or rule that is non-negotiable. For example, "Honesty is a cardinal principle that everyone should strive to uphold."
Exact(28)
This is a cardinal principle of free speech.
Flexibility is thus a cardinal principle of tactics.
The episode made budget secrecy a cardinal principle of British political life.
"That's really been a cardinal principle of our site selection," he said.
For many centuries, the protection of emissaries has been a cardinal principle enshrined in relations between nations, even ones at war.
It is a cardinal principle of international law that a state must not perform acts of sovereignty in the territory of a foreign state.
Similar(31)
Because reproducibility is a cardinal research principle, mainstream journals make material-sharing a condition of publication.
In Germany, where workers are represented on company boards and "consensus" is a cardinal social principle, it can be a particularly delicate operation.
But any pricing scheme set up to accommodate them means that some content travels first class, some coach, and that, we are told, violates a cardinal Internet principle of "network neutrality".
Only one member of the committee, Mr Adair, formerly a procurator-fiscal in Glasgow, dissents from this cardinal principle.
She developed an elaborate theology and established celibacy as the cardinal principle of the community.
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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