
theorem
  for R being non empty doubleLoopStr, a,b being Element of R holds a in
  {a,b}-Ideal & b in {a,b}-Ideal
proof
  let R be non empty doubleLoopStr, a,b be Element of R;
  {a}-Ideal c= { a,b}-Ideal & a in {a}-Ideal by Lm2,Th57,Th66;
  hence a in {a,b}-Ideal;
  {b}-Ideal c= {a,b}-Ideal & b in {b}-Ideal by Lm2,Th57,Th66;
  hence thesis;
end;
