[patio11]

There are a bunch of ways to prove this. Let's start with addition, subtraction, equality being commutative, that a + 0 = a, and that a - a = 0

Suppose that d != a - b + c. Since a = b, a - b = 0. This implies d != c. This is a contradiction, so our supposition is inaccurate. d = a - b + c

Now, suppose a + c != b + d. Plug in what we just learned. a + c != b + a - b + c. The b's cancel, leaving another contradiction. Thus, supposition inaccurate, so a + c = b + d. QED