  Tomita-Takesaki theory associates a positive operator called the "modular
operator" with a von Neumann algebra and a cyclic-separating vector. Tomita's
theorem says that the unitary flow generated by the modular operator leaves the
algebra invariant. I give a new, short proof of this theorem which only uses
the analytic structure of unitary flows, and which avoids operator-valued
Fourier transforms (as in van Daele's proof) and operator-valued Mellin
transforms (as in Zsid\'{o}'s and Woronowicz's proofs). The proof is similar to
one given by Bratteli and Robinson in the special case that the modular
operator is bounded.
