```
 We are given that a+b = a+c

   (-a) + (a+b) = (-a) + (a+c) 

   ((-a)+a) + b = ((-a)+a) + c           by BR2

   (a+(-a)) + b = (a+(-a)) + c           by BR1

            0+b = 0+c                    by BR4

      b = c                      by BR1 and BR3

```

How is (-a) added? Where does that come from? How is that step allowed/legal?