Can I presume that you know that, for any a, b, and c, "if a= b then a+ c= b+ c"?

Okay, if a= b and c= d then, first, adding c to both sides of the first equality, a+ c= b+ c. And, second, adding b to both sides of the second equality, b+ c= b+ d.

Of course, if X= Y and Y= Z then X= Z. Since a+ c= b+ c and b+ c= b+ d, then a+ c= b+ d.