theorem
  for A being set, a being object st <*a*> in 1-tuples_on A holds a in A
proof
  let A be set, a be object;
  assume <*a*> in 1-tuples_on A;
  then
A1: ex a9 being set st a9 in A & <*a*> = <*a9*> by Th133;
  <*a*>.1 = a;
  hence thesis by A1,FINSEQ_1:40;
end;
