Well...
technically that's not true.
Focal length doesn't actually change the DoF. But in the image it
looks like it does, so it's generally taught that way. You'll notice I was weasely and wrote "to increase out of focus blur," not "to decrease DoF".
You'll note, however, that 6x is
also the crop factor for a 1/2.5" sensor.
The best explanation I've seen of sensor size and its effects on noise, field of view, dynamic range, DoF, and diffraction effect is
the one on Cambridge in Colour.