theorem
  not x in still_not-bound_in p implies Ex(x,p) => Ex(y,p) is valid
proof
  assume not x in still_not-bound_in p;
  then
A1: not x in still_not-bound_in Ex(y,p) by Th6;
  p => Ex(y,p) is valid by Th15;
  hence thesis by A1,Th19;
end;
