Prove: $\alpha \rightarrow \beta, (\alpha \rightarrow \lambda) \rightarrow \beta $ proves $\beta$ in HPC

Question

I want to prove $\alpha \rightarrow \beta, (\alpha \rightarrow \lambda) \rightarrow \beta $ proves $\beta$ in HPC

I use MP and the axioms listed here: https://en.wikipedia.org/wiki/Hilbert_system

I guess that the end of the proof should look something like this:

$(\alpha\rightarrow(\beta\rightarrow\lambda)) \rightarrow ((\alpha \rightarrow \beta) \rightarrow (\alpha \rightarrow\lambda))$

$(\alpha \rightarrow \beta) \rightarrow (\alpha \rightarrow\lambda)$

$\alpha \rightarrow \lambda$

$\beta$

but I can't find out how I can get to $(\alpha\rightarrow(\beta\rightarrow\lambda))$ given my premises

would be happy for some help