as a matter of fact
US /æz ə ˈmæt.ər əv fækt/
UK /æz ə ˈmæt.ər əv fækt/

1.
de hecho, en realidad
in reality; in fact (used to emphasize the truth of a statement, often one that is contrary to what might be expected)
:
•
I thought he was angry, but as a matter of fact, he was quite pleased.
Pensé que estaba enojado, pero de hecho, estaba bastante complacido.
•
Are you going to the party? As a matter of fact, I am.
¿Vas a la fiesta? De hecho, sí.