"If a>b and b>c then a>c. For we are given [that a-b and b-c are both R+]; it therefore follows [by the first part of the order property] that a-c = (a-b) + (b-c) is in R+." (see ita-2-2-7-pg20)
We can see this result at a glance by remembering the first field property consequence that any number of numbers have a unique sum, and that parentheses may therefore be omitted or inserted at will. Then b and its additive inverse will sum to zero leaving a-c in the sum of four numbers.