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The phrase "all such assertions" is correct and usable in written English.
It can be used when referring to specific claims or statements that have been previously mentioned or are understood in the context.
Example: "In the debate, the speaker dismissed all such assertions as unfounded and lacking evidence."
Alternatives: "all these claims" or "all similar statements".
Exact(3)
Unfortunately, all such assertions in recent American history have proved greatly exaggerated.
Yet the market, immune to all such assertions of common sense, streaked ahead.
That grotesque farm bill, by itself, should put an end to all such assertions; but it only adds to the immense subsidies the heartland already receives from the rest of the country.
Similar(57)
Further investigation may challenge such assertions since all our beliefs are fallible but wholesale doubt is simply not an option.
The Pentagon rejects such assertions.
Few would dispute such assertions.
Such assertions may shock us.
The government has denied such assertions.
His performance was grounded in such assertions.
Such assertions could not be verified.
But Mr. Bonami dismissed such assertions.
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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