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The phrase "again illustrated that" is correct and usable in written English.
It can be used when referring to a previous example or evidence that reinforces a point or argument.
Example: "The recent study again illustrated that regular exercise significantly improves mental health."
Alternatives: "further demonstrated that" or "once more showed that".
Exact(4)
But it again illustrated that everything is political in an election year.
In 2004, the brief rise of Howard Dean again illustrated that little-known candidates could catch fire and raise money to compete with candidates blessed by the political establishment, but it also reinforced Iowa's importance.
First, the President has once again illustrated that he works hard to keep his campaign promises.
It once again illustrated that co-therapy with nitrates, PPIs, and H2 receptor antagonists all decreased the risk for UGIB associated with NSAID or aspirin use, although the protection conferred by nitrates was weaker than that by PPIs [ 42].
Similar(56)
In April, Joel Stein, of Bloomberg Business Week declared, "Brown killed California's deficit, awakened its economy, and provided hope that the U.S.'s biggest state can be great again," illustrating that "unsentimental, grown-up leadership can solve an economy's most intractable problems".
These latest detected changes arise before that age, but the rapid growth associated with them kicks in right at about age 12 months, once again illustrating that coincidence of events doesn't always mean their association.
New York Times Tehran bureau chief Thomas Erdbrink commented on Twitter, "According to Iran's constitution judiciary is separate power, often at odds with government polices, 'Happy' arrests again illustrate that".
The principal opposition party, the Democratic Alliance, said, "The circumstances surrounding his murder again illustrate that violent crime in South Africa is out of control, and that the government's remedies to address this scourge have failed".
This example again illustrates that we can formulate impredicative definitions in simple type theory.
The improved performance after local (study-specific) optimisation of KF again illustrates that for a multicentre study standardized administration and scanning protocols are essential.
As can be seen from the figures, the sum capacity curves for our method and the original method 1 coincide, which again illustrates that our method always achieves the same solution as the original method 1.
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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