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Discover LudwigThe phrase "the fact of" is correct and usable in written English
It can be used to refer to an established truth, reality, or condition. For example: "The fact of the matter is that we need to make a decision quickly."
Dictionary
the fact of
noun
Action; the realm of action.
Exact(59)
"Such is the fact of modern life in Washington".
After the fact, of course.
That's the fact of it.
The fact of the matter is.
The fact of it.
The fact of having written something, yes.
It's just the fact of it.
The fact of it delighted him.
The fact of the power is clear.
Plus there's the fact of being 55.
"Not to the fact of his homosexuality.
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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