Recall that we define $\alpha < \beta$ if $\alpha \in \beta$ and $\alpha \leq \beta$ if $\alpha \in \beta$ or $\alpha = \beta$. Prove that for ordinals $\alpha, \beta$, $\alpha \leq \beta$ iff $\alpha \subseteq \beta$.
(===>) If $\alpha < \beta$, then $\alpha \in \beta$ and so $\alpha \subseteq \beta$ as $\beta$ is trnasitive.
What about the other direction.?
Hint: Given ordinals $\alpha$ and $\beta$ with $\alpha \subsetneq \beta$, what can we say about the least element of $\beta \setminus \alpha$?