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The phrase "fact of" is correct and usable in written English
It is typically used to introduce a statement or piece of information that is factual and verifiable. Example: The fact of the matter is that our company has been steadily growing for the past five years.
Exact(60)
After the fact, of course.
That's the fact of it.
It is just a fact of life".
The fact of the matter is.
It's just a fact of life".
This is a fact of life.
Product placement is a fact of life.
Segregation is a fact of life.
Accept exhaustion as fact of life.
That fact, of course, cannot be forgotten.
This is an economic fact of life.
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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