This is trivial. But I could not work out a formal prove for this (using the axioms of addition).
Seems like we have to rely of definition rather than a formal prove.
Let us for the moment assume
A=B => B-A = 0 Let is call it (1)
A+C = A + C + B - A = B + C
But to prove (1) above we somewhere have to rely on A=B => A+C = B+C
Any help please?