theorem
  for A being set, a,b being object st <*a,b*> in 2-tuples_on A
   holds a in A & b in A
proof
  let A be set, a,b be object;
  assume <*a,b*> in 2-tuples_on A;
  then
A1: ex a9,b9 being object st a9 in A & b9 in A & <*a,b*> = <*a9,b9*> by Th135;
  <*a,b*>.1 = a & <*a,b*>.2 = b;
  hence thesis by A1,FINSEQ_1:44;
end;
