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Discover LudwigThe phrase "duly accepted" is correct and usable in written English
It is typically used to indicate that something has been formally acknowledged or approved in a proper manner. Example: "The proposal was duly accepted by the board during the meeting."
Exact(12)
Much to his discomfort, his threat was taken as an offer to resign and was duly accepted.
Thirty-three articles of deposition were set forth against Richard, and his abdication and deposition were duly accepted.
With the challenge duly accepted, both runners went at it, until the last third of the race.
It argued this on the basis that the flats would sell for an average of £754/sq ft, duly accepted in the officer's report (PDF).
A rare outburst of boos accompanied Liverpool's players down the tunnel after an unimpressive display which Benítez duly accepted as the worst performance of his reign and which left his side three points off the pace in Group A. "It's obviously disappointing because you have got to win your home games," said Carragher.
The fluctuations continued as a backhand down the line created a break point for Federer, which he duly accepted.
Similar(47)
An offer which -- no surprise -- he duly accepts.
They conjured an air of conviction strong enough to make it seem possible that Warren might appear from a cloud of smoke and duly accept the mantle being offered her though, at the evening's end, there was only an open bar and hors d'oeuvres.
Electoral officials duly refused to accept the PdL's slate.
Rules (Revised Helsinki Declaration, 2008) governing the conduct of human research in Nigeria and as accepted internationally were duly observed.
A year after Albert Victor's death, George duly proposed to May and was accepted.
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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