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The phrase "this case illustrates" is correct and usable in written English.
You can use it to introduce an example that demonstrates a particular point you're making. For example, "This case illustrates how certain policies can have a negative impact on the environment."
Exact(60)
This case illustrates the point well.
This case illustrates vividly why it is not compatible.
This case illustrates how we see ourselves as a society.
This case illustrates how the press can affect policymaking.
This case illustrates that tragic facts make bad law.
"This case illustrates," Justice Alito said, "that tragic facts make bad law".
This case illustrates how tricky it can be to administer rear-yard additions.
This case illustrates the danger in letting your home out to complete strangers.
As this case illustrates, it will often not been an easy one to strike.
This case illustrates the danger inherent in the principle of offsetting.
This case illustrates the heterogeneity of TTP and the difficulty of making a diagnosis of TTP.
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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