reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;

theorem Th3:
  {{}} in UN & [{{}},{{}}] in UN & [:{{}},{{}}:] in UN & op2 in UN & op1 in UN
proof
  set D = {{}};
  thus
A1: D in UN by CLASSES2:56,57;
  hence [D,D] in UN by CLASSES2:58;
A2: op2 in Funcs([:D,D:],D) by FUNCT_2:8;
  thus [:D,D:] in UN by A1,CLASSES2:61;
  then Funcs([:D,D:],D) in UN by A1,CLASSES2:61;
  hence op2 in UN by A2,ORDINAL1:10;
A3: op1 in Funcs(D,D) by FUNCT_2:8;
  Funcs(D,D) in UN by A1,CLASSES2:61;
  hence thesis by A3,ORDINAL1:10;
end;
