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as a matter of fact
01
used to introduce a statement that presents a truth or reality, often to clarify or emphasize something
Пример
He claimed it was the largest in the city, but as a matter of fact, there are several larger buildings in the downtown area.
As a matter of fact, I did see him at the store earlier today.
You may believe it's a rumor, but as a matter of fact, the company has officially announced the merger