A+B = C
That means: A = C-B
Let's look at:
         A*C=A*C
<=>  A*(A+B) = (C-B)*(A+B)
<=>  A*A+A*B = A*C+B*C-A*B-B*B
take A*C on both sides and you'll get
        A*A+A*B-A*C = B*C-B*B-B*A
<=> A*(A+B-C) = (-1)*B*(A+B-C)
Divide with (A+B+C) and you get the implication:
A+B=C => A=(-B)