theorem
  for A being set,a,b,c being object st <*a,b,c*> in 3-tuples_on A holds
  a in A & b in A & c in A
proof
  let A be set,a,b,c be object;
A1: <*a,b,c*>.3 = c;
  assume <*a,b,c*> in 3-tuples_on A;
  then
A2: ex a9,b9,c9 being object
   st a9 in A & b9 in A & c9 in A & <*a,b,c*> = <*a9,
  b9,c9*> by Th137;
  <*a,b,c*>.1 = a & <*a,b,c*>.2 = b;
  hence thesis by A2,A1,FINSEQ_1:45;
end;
