Order_Isomorphism_between_Wosets_is_Unique

Let $\struct {S_1, \preceq_1}$ and $\struct {S_2, \preceq_2}$ be wosets. Let $\struct {S_1, \preceq_1} \cong \struct {S_2, \preceq_2}$, that is, let $\struct {S_1, \preceq_1}$ and $\struct {S_2, \preceq_2}$ be order isomorphic. Then there is exactly one mapping $f: S_1 \to S_2$ such that $f$ is an order isomorphism.