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The phrase "a simple consequence of" is correct and usable in written English.
It can be used to indicate that something is a straightforward result or outcome of a particular situation or condition.
Example: "The increase in sales was a simple consequence of the new marketing strategy we implemented."
Alternatives: "an obvious result of" or "a direct outcome of".
Exact(59)
The Pacers' scoring success is not a simple consequence of their size, though that certainly helped.
Encyclopædia Britannica, Inc. Glacier flow is a simple consequence of the weight and creep properties of ice.
And this, moreover, as a simple consequence of the growing mass of facts on this most marvellous organ, accumulated in the last four decades.
It is a simple consequence of for.
A simple consequence of Theorem 21 is the following one.
Proof (a) It is a simple consequence of Corollary 2.7.
We start with a simple consequence of asymptotic contractiveness.
Here, we point out a simple consequence of Theorem 3.1.
This fact is a simple consequence of (1.1).
This dramatic effect of observation is, in fact, a simple consequence of Bohmian mechanics.
For the case of (n =2), the equality (iii) is a simple consequence of Eq. (3.2).
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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