theorem
  |- f^<*All(x,p)*> iff |- f^<*'not' Ex(x,'not' p)*>
proof
  thus |- f^<*All(x,p)*> implies |- f^<*'not' Ex(x,'not' p)*>
  proof
    assume |- f^<*All(x,p)*>;
    then |- f^<*All(x,'not' 'not' p)*> by Th65;
    then |- f^<*'not' 'not' All(x,'not' 'not' p)*> by Th53;
    hence thesis by QC_LANG2:def 5;
  end;
  assume |- f^<*'not' Ex(x,'not' p)*>;
  then |- f^<*'not' 'not' All(x,'not' 'not' p)*> by QC_LANG2:def 5;
  then |- f^<*All(x,'not' 'not' p)*> by Th54;
  hence thesis by Th66;
end;
