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The phrase "as they explained" is correct and commonly used in written English.
It is typically used to introduce an explanation or a reason for something that has been mentioned previously in the sentence or in the context. Here is an example: "The students were struggling with the difficult math problem, but as they explained, they had not yet learned the necessary formula to solve it."
Exact(60)
Both leaders spoke for about 40 minutes, adopting professorial tones as they explained the conflict.
As they explained it to Kelley, he remembers them repeating, "It was the best option available".
As they explained, it's a game: the first singer to fall out of rhythm loses.
Both leaders have faced a backlash within their parties as they explained the details to members.
A parade of Democrats, who have long pressed for new gun laws, rose to praise the bill as they explained their votes.
As they explained in an interview from their home in Tamarac, Fla., the couple became engaged during remarks at a wedding in 1940.
But the founders' ambitions are lofty, as they explained in an interview Monday in the elaborate presidential dining room on the lush U.S.C. campus.
As they explained in a blog post on the Facebook Engineering Department page, graph search solves a problem of Facebook's own making: it has collected so much information.
They would sort of giggle as they explained to a foreigner aspects of collective living, like car sharing or the former king taking a tram".
He led them in and as soon as they explained they were from the Army I knew the worst had happened.
It glimmered in their eyes as they explained dishes and brought giddy laughter to guests who ate langoustines with their hands, smearing green sauce across giant rocks.
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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