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The phrase "self-evident fact" is correct and usable in written English.
You can use it when referring to something that is obvious, undeniable, and widely accepted. For example, "It is a self-evident fact that the sun rises in the east each morning."
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Despite this self-evident fact, the available evidence has generally shown low adherence rates to antidepressant treatment in patients with a major depressive disorder [ 1- 3].
Further judicial process will not change this self-evident fact and will only result in confusion and disorder.
A government minister, presented with some self-evident fact – benefit sanctions cause people to go hungry – blithely rejects it.
In view of this self-evident fact, it is highly improbable that the defendant gave libelants rotten and unserviceable nets with which to fish.
She said: "Peter Dutton is pointing out the self-evident fact that it costs a great deal of money to settle people in Australia".
How foolishly apocalyptic those apprehensions seem by daylight, when the self-evident fact of the streets and the people on them is its own justification, its own insurance.
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I don't want to be in danger of being presented as a "suspicious" journalist, just for stating self-evident facts, by the very propagandists of the power structure that brought my country on the edge.
It was because Stalin, despite the self-evident facts, thought that the war had not yet started, that this was only a provocative action on the part of several undisciplined sections of the German army, and that our reaction might serve as a reason for the Germans to begin the war.
Against this conventional Christian perspective Camus asserts what he regards as self-evident facts: that we must die and there is nothing beyond this life.
If such a self evident fact can be denied, why expect them to believe in science or even history?
In this world, Hughes's observation is the last self-evident truth: Facts are a thing of the past.
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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