how to prove $ B = ( \beta \Rightarrow \gamma) \Rightarrow (\alpha \Rightarrow \beta)\Rightarrow \alpha\Rightarrow \gamma $ using natural deduction

Question

I tried to follow a similar question solving another statement using natural deduction but it still seems hard to understand every time I get a different solution I can't figure out a methodology to solve these kinds of statements. Can you guys explain to me how to solve this with a methodology to follow for any other statement so I can be able to solve them my self?

This is the statement I'm trying to solve:

$$ B = ( \beta \Rightarrow \gamma) \Rightarrow (\alpha \Rightarrow \beta)\Rightarrow \alpha\Rightarrow \gamma. $$

Answer 1

1) $(β ⇒ \gamma)$ ---assumed [a]

2) $(α ⇒ β)$ --- assumed [b]

3) $\alpha$ --- assumed [c]

4) $\beta$ --- from 3) and 2) by ⇒-elimination

5) $\gamma$ --- from 4) and 1) by ⇒-elimination

6) $\alpha ⇒ \gamma$ --- from 3) and 5) by ⇒-introduction, discharging [c]

7) $(α ⇒ β) ⇒ (\alpha ⇒ \gamma)$ --- from 2) and 6) by ⇒-introduction, discharging [b]

8) $(β ⇒ \gamma) ⇒ ((α ⇒ β) ⇒ (\alpha ⇒ \gamma))$ --- from 1) and 7) by ⇒-introduction, discharging [a].