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The phrase "proof by" is correct and can be used in written English.
It is typically used in the context of providing evidence or justification for something, often in a logical or argumentative sense. Example: The defendant's lawyer presented a strong proof by using DNA evidence to support their claim of innocence.
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PROOF By David Auburn.
Her argument amounts to Proof by Anecdote.
CHATHAM PLAYERS "Proof," by David Auburn.
L. HOWARD FOX STUDIO THEATER "Proof" by David Auburn.
ORADELL "Proof," by David Auburn Bergen County Playerss.
PROOF, by Jeff Reich; directed by Kevin Confoy.
And he offered proof by starting light training yesterday.
SUSSEX Tri-State Actors Theater "Proof," by David Auburn.
Proof by contradiction.
In most cases, it's proof by example.
We use proof by contradiction.
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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