reserve F,H,H9 for ZF-formula,
  x,y,z,t for Variable,
  a,b,c,d,A,X for set;
reserve E for non empty set,
  f,g,h for Function of VAR,E,
  v1,v2,v3,v4,v5,u5 for Element of VAL E;

theorem
  H is universal implies for f holds (f in St(the_scope_of H,E) & for g
  st for y st g.y <> f.y holds bound_in H = y holds g in St(the_scope_of H,E) )
  iff f in St(H,E)
proof
  assume H is universal;
  then H = All(bound_in H,the_scope_of H) by ZF_LANG:44;
  hence thesis by Th6;
end;
