Category:Order Isomorphisms

Let $\left({S, \preceq_1}\right)$ and $\left({T, \preceq_2}\right)$ be ordered sets.
Let $\phi: S \to T$ be a bijection such that:
$\phi: S \to T$ is order-preserving
$\phi^{-1}: T \to S$ is order-preserving.
Then $\phi$ is an order isomorphism.