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'And thus' is correct and usable in written English
You can use it to refer to a consequence or conclusion that follows from a previous statement. For example: "The teacher gave us an explanation of the concept, and thus we were able to understand it much better."
Exact(60)
And thus it proved.
And thus, time to divorce.
And thus do no Ryan.
And, thus, to care.
And thus, compassionate conservatism.
And thus more fascinating.
And thus it remains.
"And thus illegal".
And thus the court case.
"And thus illegal," Lynch replied.
And thus hardcore became mainstream.
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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