Lemma regarding constructible universe

Question

How does $\alpha \subset L_{\alpha}$ follow from the lemma : whenever $\alpha < \beta ,\alpha , L_{\alpha} \in L_{\beta}$ ?

Answer 1

If $\gamma\in\alpha$, then $\gamma<\alpha$, so $\gamma\in L_\alpha$ (replacing $\alpha$ and $\beta$ in your lemma by $\gamma$ and $\alpha$, respectively).