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"firstly approved" is correct and usable in written English.
It is usually used to introduce the first of several items or actions. For example, "Before the new project could be started, the plans had to be firstly approved by the board of directors."
Exact(3)
The experimental data were firstly approved by Ostwald de Waele model, and then used to develop a novel mathematical model, correlating the volume fraction of the solid phase and the operating temperature to the viscosity of the composite nano-fluid.
The research proposal was firstly approved by the Institutional Review Board of the coordinating center and then confirmed by IRB of each other participating center.
Subsequently, the National Development and Reform Commission firstly approved three BOT infrastructure projects in 1996, including Chengdu No.6 Water Supply BOT Plant (B), Guangxi Laibin Power BOT Plant, and Changsha Wangcheng Power BOT Plant (failed).
Similar(57)
Rat gene symbols are compared with firstly human symbols approved by HGNC [ 19] and secondly mouse gene symbols obtained from MGI [ 18].
Firstly, elucidation of the disease mechanism enabled identification of the molecular target(s) which catalysed pharmaceutical research and resulted in Gleevec® (Novartis) as the first FDA approved BCR-ABL inhibitor.
Firstly the study proposal was screened and approved by the Ethics Review Panel of the European Commission as part of the project evaluation phase in 2009.
Firstly, among the other eight candidates who are approved to run for presidency, Jalili is by far the most outspoken one.
Firstly, drug-based therapy has improved when the medically approved drugs or previously abandoned drugs have been rediscovered for other indications.
Firstly, to abandon the tiebreaker regimen in favour of a WHO approved serial or parallel algorithm.
We studied firstly the evaluation reports for 40 drugs from a list of 170 drugs that had been approved by the French National Medicines Assessment Committee between January 2008 and January 2011.
He said Sunday's Istanbul rally was the third time the opposition had come together in large numbers - firstly in the 2013 protests in Istanbul's Gezi Park, then in April over the referendum which narrowly approved Erdogan's new powers.
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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