theorem
  p is existential implies Vars(p,V) = Vars(the_argument_of the_scope_of
  the_argument_of p, V)
proof
  set p1 = the_argument_of the_scope_of the_argument_of p;
  set x = bound_in the_argument_of p;
  assume p is existential;
  then p = Ex(x,p1) by QC_LANG2:40;
  then p = 'not' All(x,'not' p1) by QC_LANG2:def 5;
  then Vars(p,V) = Vars(All(x,'not' p1), V) by Th39
    .= Vars('not' p1, V) by Th44
    .= Vars(p1, V) by Th39;
  hence thesis;
end;
