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"By this" is correct and can be used in written English.
You can use it to refer generally to something that has been previously mentioned or to a situation that is currently in progress. For example: "I've been following my diet for two weeks now and by this I can already see some results."
Exact(60)
By this, she meant expensive.
By this definition, the Internet is magic.
By this standard, "Argo" is definitely successful.
By this point, Ambrose was getting defensive.
Not by this bonbon.
Followed by this.
I am pained by this.
We're inundated by this stuff.
I'm dazzled by this director.
"I'm really surprised by this.
We are democratized by this.
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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