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The phrase "a consequence of the fact" is correct and usable in written English.
It can be used when discussing the result or outcome that arises from a specific situation or condition.
Example: "The increase in pollution levels is a consequence of the fact that more cars are on the road."
Alternatives: "a result of" or "an outcome of".
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.
"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.
Their early interviews were monosyllabic to the point of churlishness – a consequence of the fact that they have never liked talking about themselves.
This is a consequence of the fact that this is the way the myth is told.
which is a consequence of the fact that each subchannel is memoryless.
This is a consequence of the fact that there is no total flow.
The invariance of the cone is a consequence of the fact that the nonlinearities are nonnegative.
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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