reserve U for Universe;

theorem Th1:
  for X,Y being set st X in U & Y in U for R being Relation of X,Y holds R in U
proof
  let X,Y being set;
  assume that
A1: X in U and
A2: Y in U;
  [:X,Y:] in U by A1,A2,CLASSES2:61;
  hence thesis by CLASSES1:def 1;
end;
