Depth of field is affected by two things: aperture and subject distance.
No, dof is affected by two things, aperture size (not number) and subject magnification.
A 17mm and 200mm shot from the same place with the same aperture value have different dof, your statement says they would be the same.
Ok good point. I was taking FL as static, basically trying to distinguish lens from sensor. But that is more accurate, I will edit.
Well we still aren't quite there. If you take the same picture from the same place with the same lens and settings and on a crop and ff cameras, then make two prints the same size, the image is different (obviously) and the dof is less in the crop camera image.
If you have two different sized prints, such that the subjects were the same size then the dof would be the same from both cameras.
DOF is dependent on magnification, to get a same sized print you have to enlarge the crop camera more so it has less dof.
It isn't until people accept that dof is subjective and dependent on magnification, that it clicks that crop cameras can have, more, less, or the same, dof as a ff camera.
Maybe it will click tomorrow... but tonight... I'm enjoying my gambling winnings from a triple overtime game.