for A being non empty set
for x, y, z being Element of (RRing A) holds
( x + y = y + x & (x + y) + z = x + (y + z) & x + (0. (RRing A)) = x & ex t being Element of (RRing A) st x + t = 0. (RRing A) & x * y = y * x & (x * y) * z = x * (y * z) & x * (1. (RRing A)) = x & (1. (RRing A)) * x = x & x * (y + z) = (x * y) + (x * z) & (y + z) * x = (y * x) + (z * x) )