theorem Th164:
  z <> x implies (Ex(z,G) = Ex(z,H)/(x,y) iff G = H/(x,y))
proof
  assume z <> x;
  then 'not' G = ('not' H)/(x,y) iff All(z,'not' G) = All(z,'not' H)/(x,y) by
Th159;
  hence thesis by Th156;
end;
