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The phrase "has a firm knowledge of" is correct and usable in written English
You can use it when describing a person who has a strong understanding of something, for example: Jane has a firm knowledge of the scientific principles behind climate change.
Exact(2)
Mr. Cavanaugh, who was a frequent contributor to The New York Times, has a firm knowledge of the fight game, and his description of Tunney's 10-round upset in Philadelphia crackles.
Mr. O'Day is no disciple of City Ballet's founding father, George Balanchine, although he has a firm knowledge of the classical idiom and uses it with a welcome brashness.
Similar(58)
Have a firm knowledge of the times that you live in and of what has to be done.
However, before such strategies are adopted researchers must have a firm knowledge of the vector's ecology and its genetic basis.
But it also meant a firm knowledge of prior demand.
A senior American official who has been briefed extensively on the intelligence noted in recent days that Washington has firm knowledge of only 19 of the 42 suspected chemical weapons sites.
The basis of understanding this technique has to be firm knowledge of anatomy, topology and moreover of sonoanatomy.
Being a comparatively new approach to coastal management, this increased usage has occurred against a background of little firm knowledge of the longer term impacts.
He has an encyclopedic knowledge of mouthpieces.
To the best of our knowledge, in 2007, phenotyping or genotyping for pharmacogenetic polymorphisms had a firm regular place in only a few hospitals or doctor's offices.
Because of their long relationship with the firm, family owners typically have a deep knowledge of the industry, the firm, and its stakeholders.
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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