Suppose G is an additive group with the following properties:

1) x+(y+z) =(x+y) +z for all x,y,z in G

2) There exists 0 such that: x+0 =0+x = x for all x in G

3) For all x in G there exists -x such that : x+(-x) = (-x)+x =0

Now do we need to prove that 0 and -x are unique ,before we prove that:

-(x+y) = (-y)+(-x) and -(-x) = x