Prove for all the ordinals α and β that ( α∗β, ∈) ≃ (α x β, <)

Question

Prove for all the ordinals $\alpha$ and $\beta$ that ( $\alpha * \beta$, $\in$) $\simeq$ ($\alpha$ x $\beta$, <), where < is an antilexicographic device on $\alpha$ x $\beta$.