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The phrase "the same principles apply" is correct and usable in written English.
You can use this phrase when you want to indicate that the same rules or standards are relevant in different situations. For example, "In both of these cases, the same principles apply: be honest and stay true to yourself."
Exact(59)
The same principles apply.
The same principles apply today".
The same principles apply to alcoholism.
The same principles apply for athletic measurables.
The same principles apply to treating cancer.
The same principles apply, though, apparently.
Yet the same principles apply to the environment.
The same principles apply to the "paradox of deleverage".
But the same principles apply to swimming, tennis, bicycling or basketball.
"Legislative data is far more complex," Mr. Hoyer said, "but the same principles apply.
But the same principles apply to decision making at lower levels.
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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