The source knows that he's talking about. It is common sense. We are both seniors in mechanical engineering.
You have a set amount of air at atmospheric pressure inside a cylinder. The volume of the cylinder is reduced with the same amount of air in it. The pressure is no longer atmospheric, it has increased.
Here is another example that is easier to understand. There is 500lb resting on a 1in x 1in area. That would be 500psi. That area is then reduced to a 0.5in x 0.5in area. The pressure is now 2000psi.
