reserve Q,Q1,Q2 for multLoop;
reserve x,y,z,w,u,v for Element of Q;

theorem Th47:
  for Q2 being multLoop holds
  for f being homomorphic Function of Q,Q2 holds
  for x,y holds
  y in x * lp (Ker f) iff f.x = f.y
proof
  let Q2 be multLoop,f be homomorphic Function of Q,Q2,x,y;
  y in x * lp (Ker f) iff y in x * Ker f by Th19;
  hence y in x * lp (Ker f) iff f.x = f.y by Th46;
end;
