I'm reading Kuratowski's "Set theory", and following the next definition from the Chapter 7:
"An order number $\alpha$ is less than $\gamma$ iff some $\alpha$-set is isomorphic to an initial segment of some $\gamma$-set." Now, it's intuitively clear that if some $\alpha$-set is a subset of $\gamma$-set, then $\alpha \leq \gamma$. But how can I prove it using the definition?