Rational Homology Ribbon Cobordism is a Partial Order

We prove that rational homology ribbon cobordism defines a partial order on the set of homeomorphism classes of closed, connected, oriented 3-manifolds. More precisely, if $W_0\le W_1$ and $W_1\le W_0$, then $W_0$ and $W_1$ are homeomorphic by an orientation preserving homeomorphism.