
theorem
  for t,u being set st t c= u holds TWOELEMENTSETS(t) c= TWOELEMENTSETS(u)
proof
  let t,u be set;
  assume
A1: t c= u;
  let e be object;
  assume
A2: e in TWOELEMENTSETS(t);
  then e is finite Subset of t by Th8;
  then
A3: e is finite Subset of u by A1,XBOOLE_1:1;
  ex x,y being object st x in t & y in t &( not x=y)& e={x,y} by A2,Th8;
  hence thesis by A1,A3,Th8;
end;
