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"a first necessity" is a correct and usable phrase in written English.
It can be used to describe something that is essential, vital, or necessary in a particular situation or context. Example: In a survival situation, finding shelter is a first necessity for staying alive.
Exact(1)
Despite unclear upstream mechanisms, NLRP3 is expressed at limiting levels in macrophages or dendritic cells, possibly to avoid unintended inflammation, and requires a PRR-dependent priming signal via TLRs as a first necessity for its subsequent activation (Bauernfeind et al, 2009; Juliana et al, 2012).
Similar(59)
A second necessity is to give interest rate relief on sovereign debt, to lessen the ramifications of the excessive debt in the financial system.
The first necessity is a development of a guideline for economic evaluations.
The first necessity for a blank slate is an omnipotent eraser, and the guillotine was the one at hand.
Whether the structure is a single-family house or a thirty-story building, the first necessity is that every room have light and air.
The first necessity is a reform of the Greek economic structure.
A visit to the camp barber was the first necessity for the recruits, where a close "number one" cut was the only style on offer.
The first necessity was to establish a legitimate basis of action.
The first necessity for organizational health is building a cohesive leadership team.
The first necessity for Mrs. Clinton — high turnout — is a virtual certainty.
High ceilings were the first necessity but plenty of other smaller trivial things needed a reworking, too.
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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