Page "Proper time" Paragraph 44

So the total proper time for observer B to go from ( 0, 0, 0, 0 ) to ( 5 years, 4. 33 light-years, 0, 0 ) to ( 10 years, 0, 0, 0 ) is 5 years.

Thus it is shown that the proper time equation incorporates the time dilation effect.

In fact, for an object in a SR spacetime traveling with a velocity of v for a time, the proper time experienced is