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The phrase "are valid only in" is correct and usable in written English.
It can be used to specify the conditions or contexts in which something is applicable or accepted.
Example: "These rules are valid only in the context of this competition."
Alternatives: "apply solely in" or "are applicable exclusively in".
Exact(22)
However, they are valid only in their own specific situations.
The marriages are valid only in Spain and in other countries that accept same-sex marriages.
The arrest warrants are valid only in France, meaning the two men face arrest if they go there.
Formulations proposed to alleviate this have only been partly successful and are valid only in certain specific situations.
Strictly speaking, Newton's laws of motion are valid only in a coordinate system at rest with respect to the "fixed" stars.
The new tests are also not required to meet the strict standards of safety and effectiveness established by the F.D.A., and they are valid only in singleton pregnancies.
Similar(38)
The proposed surrogate function is valid only in the specific ranges of the design variables.
Simply ignoring those subjects with unknown membership is valid only in the MCAR situation.
This observation is valid only in the case of DLC/100Cr6 tribological contact.
The patent is valid only in this country; the foundation has also applied for patents in Europe.
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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