as a matter of fact

used to introduce a statement that presents a truth or reality, often to clarify or emphasize something

As a matter of fact, I did see him at the store earlier today.
The matter of the fact is, we need more funding to complete this project successfully.
He claimed it was the largest in the city, but as a matter of fact, there are several larger buildings in the downtown area.
You can argue all you want, but the matter of the fact is, the rules were clearly broken.
You mentioned she wasn't interested; as a matter of fact, she expressed keen interest in joining the project

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