theorem
  H is existential implies H is negative & the_argument_of H is
  universal & the_scope_of the_argument_of H is negative
proof
  given x,H1 such that
A1: H = Ex(x,H1);
  the_argument_of 'not' All(x,'not' H1) = All(x,'not' H1) & the_scope_of
  All(x,'not' H1) = 'not' H1 by Th1,Th7;
  hence thesis by A1;
end;
