Ack, sorry to hear this @daan. I know the feeling, my dad died in 2000. It's the only time I have seen a dead person and that cold feeling... I remember only too well.
His was sudden same as yours, it's better than a long drawn out death but that's no consolation.
Yeah, in a way it's better like this. He was suffering from COPD and the alternative was spending months in a hospital and slowly deteriorating. I've kinda made peace with the situation, my brother's a bit more in shock still.