theorem
  not x in still_not-bound_in q implies ( Ex(x,p) => q is valid iff All(
  x,p => q) is valid )
proof
  assume not x in still_not-bound_in q;
  then (Ex(x,p) => q) <=> All(x,p => q) is valid by Th81;
  hence thesis by Lm15;
end;
