Natural deduction: understanding bottom elimination (¬e)
Usually in practice we weld the two steps together and just say that from $p$ and $\lnot p$ anything follows, but in formal logic this is a combination of two rules of inference:


$p$ and $\lnot p$ both together entail falsehood $\bot$,
from $\bot$ anything follows.


These are precisely lines 9 and 10 in your proof.

We often take $\lnot p$ to be an abbreviation for $p \Rightarrow \bot$, in which case the rule "from $p$ and $\lnot p$ follows $\bot$" is just a special case of modus ponens "from $p$ and $p \Rightarrow r$ follows $r$".