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The phrase "the first example is" is grammatically correct and can be used in written English.
You can use this phrase when referring to a particular example of something that is being discussed. For example, "The first example of a successful business strategy is to focus on customer satisfaction."
Exact(60)
The first example is provided by an IS upstream the gtf gene, PFREUD_19370.
The first example is "Scissors and a cooking pan".
The first example is an illustration of pleasure in quantity, the second in variety.
The first example is one in which business firms see increased opportunities for profitable investment.
The first example is called parameter identification.
The first example is inspired by [17].
The first example is an agitator/mixer scale-up.
The first example is of course in different cultures.
The first example is a high speed slider crank mechanism with a flexible connecting rod.
The first example is a plate with an interface between hard and soft materials.
The first example is an in situ electrical transport measurement of a bundle of carbon nanotubes.
More suggestions(17)
the first instance is
the nearest example is
the first models is
the first cases is
the strongest example is
the earliest example is
the biggest example is
the worst example is
the largest example is
the first lessons is
the former case is
foremost example is
one case is
the first option is
the first type is
the first example shows
the first illustration of the
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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