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"independently of" is a correct phrase and is commonly used in written English.
It is typically used to indicate that something is not influenced or affected by something else. Example: "The company's profits increased independently of the economic downturn."
Exact(59)
Independently of the factories.
independently of Section 301".
"Erik climbed independently of us.
It acts independently of ministers.
In theory, they operate independently of candidates.
They were operated independently of each other.
The story played independently of my intentions.
We arrived independently of one another.
More may be travelling independently of package tours.
Palmer said Gore had "made his comments independently of me".
Its dynamics continue independently of whether or not we exist.
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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