reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;

theorem Th10:
  product {} = {{}}
proof
  thus product {} c= {{}}
  proof
    let x be object;
    assume x in product {};
    then ex g st
    x = g & dom g = dom {} &
     for y being object st y in dom {} holds g.y in {} .y by Def5;
    then x = {};
    hence thesis by TARSKI:def 1;
  end;
  let x be object;
  assume x in {{}};
  then
A1: x = {} by TARSKI:def 1;
  for y being object st y in dom {} holds {} .y in {} .y;
  hence thesis by A1,Th9;
end;
