reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem
  for X,Y being non empty set st
  Funcs(X,Y) is Element of U holds X is Element of U
  proof
    let X,Y be non empty set;
    assume
A1: Funcs(X,Y) is Element of U;
    set y = the Element of Y;
A2: [:X,{y}:] c= union Funcs(X,Y) by Th5;
    union Funcs(X,Y) in U by A1,CLASSES2:59;
    then [:X,{y}:] is Element of U by A2,CLASSES4:13;
    hence thesis by CLASSES4:40;
  end;
