As a matter of fact
Definition 1 of 2
Pro Tip 1/3Emphasizing Reality
Used to emphasize that what you're saying is true or correct, contrary to what might be assumed. 
He might look unfriendly, but as a matter of fact, he's very kind.
Pro Tip 2/3Correcting Assumption
Use it to rectify a misunderstanding or correct a false assumption someone might have. 
You might think I'm busy, but as a matter of fact, I'm free all afternoon.
Pro Tip 3/3Strengthens Statements
It can be used to strengthen a statement or argument you're making. 
As a matter of fact, our research proves that this method is more effective.