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"consequence of the fact" is a correct and usable phrase in written English.
It is typically used to introduce a result or outcome that is directly caused by a certain fact or situation. Here is an example: "Many experts believe that the increasing use of technology in education is a consequence of the fact that young people today are more comfortable with digital tools than previous generations."
Exact(60)
"It's a consequence of the fact that musical education is missing," he said.
But this is itself a consequence of the fact that companies invest much less in training than they used to.
The second problem is a consequence of the fact that, being so small, hydrogen is also exceptionally light.
That is an inevitable consequence of the fact that human rights are only one of many foreign-policy concerns.
"And that's a consequence of the fact that discussions with the European Union are more advanced than they are with the UK".
Or is it simply a consequence of the fact that among any group of American intellectuals you'll find Jews overrepresented because they are a well-educated minority?
That's actually a consequence of the fact that the photon has no mass, and so can only ever travel at the speed of light.
It's made its voice louder, which is a natural consequence of the fact that it brings value to a notion of separate identity".
It is the consequence of the fact that intimate relationships are likely to be less safe for women than for men.
What no one ever says when covering these stories is that rationing is the inevitable consequence of the fact that people won't pay more in taxes.
In part, this is just a natural consequence of the fact that the globe floats through space under the watchful eye of weather satellites.
More suggestions(16)
effects of the fact
consequences of the fact
consequence of the facts
ramifications of the fact
a by-product of the fact
consequence of the data
implications of the fact
a result of the fact
result of the fact
results of the fact
repercussions of the fact
consequence of the lawyer
consequence of the public
consequence of the reshuffle
consequence of the way
consequence of the lack
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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