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Discover LudwigThe phrase "by that statement" is correct and usable in written English.
You can use it to refer to a statement that has just been made. For example: "He claimed that he was innocent, but I'm not sure I believe him - by that statement, I'm inclined to think he's guilty".
Exact(45)
I feel embarrassed by that statement".
"I stand by that statement".
I was very moved by that statement.
I would stand by that statement.
Mrs. Newburger was taken aback by that statement.
Rich Halberg, a spokesman for Allstate, said he was puzzled by that statement.
Similar(13)
To judge by appearances, that statement covered her wardrobe as well.
I'm not insinuating anything with that statement by the way.
"We come to that statement by examining our battle damage assessment up until now," Warren said.
We finalize the proof by noticing that the statement of the theorem directly follows from Theorem 3.1.
That statement by Mr. Holscher was not challenged.
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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