theorem Th1: :: ALGSTR_1:1

for L being non empty addLoopStr
for a, b being Element of L st ( for a being Element of L holds a + (0. L) = a ) & ( for a being Element of L ex x being Element of L st a + x = 0. L ) & ( for a, b, c being Element of L holds (a + b) + c = a + (b + c) ) & a + b = 0. L holds
b + a = 0. L