A newer reference is
Unbounded Self-adjoint Operators on Hilbert Space by Konrad Schmüdgen
http://link.springer.com/book/10.1007%2F978-94-007-4753-1
The desired result is a consequence of Theorem 5.7 (p.89) combined with Proposition 15.14 (p.358), Definition 4.2 (p.66), Theorem 4.6 (p.68) and the unlabeled displayed definition at the bottom of page 73.