theorem
  not x in still_not-bound_in p implies ( p => Ex(x,q) is valid iff Ex(x
  ,p => q ) is valid )
proof
  assume not x in still_not-bound_in p;
  then (p => Ex(x,q)) <=> Ex(x,p => q) is valid by Th85;
  hence thesis by Lm15;
end;
