as a matter of fact

Từ điển Oxford Advanced Learner 8th

as a matter of ˈfact idiom
1. used to add a comment on sth that you have just said, usually adding sth that you think the other person will be interested in
• It's a nice place. We've stayed there ourselves, as a matter of fact.
2. used to disagree with sth that sb has just said
Syn: ↑actually
• ‘I suppose you'll be leaving soon, then?’ ‘No, as a matter of fact I'll be staying for another two years.’
Main entry: ↑matter_idiom