reserve x,y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve f for RingMorphismStr;
reserve G,H,G1,G2,G3,G4 for Ring;
reserve F for RingMorphism;
reserve V for Ring_DOMAIN;

theorem Th18:
  for x being Element of RingObjects(UN) holds x is strict Ring
proof
  let x be Element of RingObjects(UN);
  consider u being set such that
  u in UN and
A1: GO u,x by Def16;
  ex x1,x2,x3,x4,x5,x6 being set st u = [[x1,x2,x3,x4],x5,x6] & ex G being
strict Ring st x = G & x1 = the carrier of G & x2 = the addF of G & x3 = comp G
  & x4 = 0.G & x5 = the multF of G & x6 = 1.G by A1;
  hence thesis;
end;
