theorem
  G is independent implies Ex('not' All(a,A,G),B,G) = Ex('not' All(a,B,G ),A,G)
proof
A1: 'not' All(All(a,A,G),B,G) = Ex('not' All(a,A,G),B,G) by BVFUNC_2:18;
  assume G is independent;
  hence thesis by A1,Th15;
end;
