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The phrase "first appearance of" is grammatically correct and commonly used in written English.
It refers to the initial instance of something appearing or being introduced. Example: "The first appearance of smartphones revolutionized the way we communicate." In this sentence, "first appearance of" indicates the initial introduction of smartphones and how it had a significant impact on communication.
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Philharmonic's first appearance of the season..
It was her first appearance of the campaign.
It has been nearly 20 years since the first appearance of robotics in the operating room.
Now these events happened on the first appearance of the Persians before Miletus.
That utopian goal has been with us since the first appearance of the Dark Satanic Mills.
The Ediacaran Period witnessed the first appearance of macroscopic animal life in Earth's history.
It was Beck's first appearance of the series, and it was a disaster.
Nevertheless, the preferred explanation for the first appearance of hominins outside Africa has remained virtually unchanged.
The historic first appearance of men's and women's British teams has garnered plenty of column inches.
On Saturday, Paul Pogba made his first appearance of the weekend, on the cover of L'Equipe.
The GSSP marks the first appearance of the graptolites Akidograptus ascensus and Parakidograptus praematurus.
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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