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The phrase 'is proof that' is grammatically correct and usable in written English.
It is used to indicate that something is the evidence or substantiation of a certain statement or belief. For example: The large increase in population over the past few years is proof that the city is growing rapidly.
Exact(60)
China is proof that they operate independently.
"This is proof that we are deep inside the kitchen".
He is proof that judicial nominations matter, especially for women.
But Medellín is proof that they're not, and shouldn't be.
Here is proof that Americans are still awesome.
"It is proof that dreams do come true.
That is proof that the plan is working.
But to others, this is proof that they didn't.
It is proof that only effective government works.
Learning lines is proof that your memory isn't going anywhere.
To them, this is proof that the organization is nefarious.
More suggestions(18)
is testimony that
is testament that
is rationale that
is tests that
is demonstration that
is testing that
bears proof that
is evidences that
is verification that
is documentation that
is validation that
becomes proof that
exactly proof that
was evidence that
is a demonstration that
was testimony that
are evidence that
is evidence that
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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