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Discover Ludwig"not backing down" is a perfectly correct and usable expression in written English.
You can use it to express a person's refusal to compromise or give in to someone or something. For example: In the face of adversity, the team leader refused to give up and was adamant about not backing down.
Exact(54)
We are not backing down".
Fox is not backing down.
Obama aides were not backing down.
We're not backing down from that".
I'm not backing down, either.
LVMH is not backing down.
"Hollande is not backing down.
We're not backing down to anybody.
But Guinea's government is not backing down.
I'm not backing down from that system.
But Johnson is not backing down.
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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