Is my proof by natural deduction for $(p\rightarrow (q\rightarrow r))\rightarrow (q\rightarrow (p\rightarrow r))$ correct?

Question

1. $\left(p\rightarrow\left(q\rightarrow r\right)\right)$---premise
2. q---assumption
3. p---assumption
4. $q\wedge p$---by $\wedge$-Intro from 2 and 3
5. q---by $\wedge$-elim from 4
6. p---by $\wedge$-elim from 4
7. $q\rightarrow r$---by $\rightarrow$-elim from 1 and 6
8. r------by $\rightarrow$-elim from 5 and 7
9. $p\rightarrow r$---by $\rightarrow$-Intro from 3 and 8
10. $q\rightarrow\left(p\rightarrow r\right)$---by $\rightarrow$-Intro from 2 and 9
11. $\left(p\rightarrow\left(q\rightarrow r\right)\right)\rightarrow\left(q\rightarrow\left(p\rightarrow r\right)\right)$---by $\rightarrow$-Intro from 1 and 10

Also is there any other way to do this proof by natural deduction?

Answer 1

eliminating 4,5 and 6 which were unnecessary, the correct proof is:

1. $\quad\bullet\; \left(p\rightarrow\left(q\rightarrow r\right)\right)$ --- premise
2. $\quad\bullet \quad\bullet\;q$ --- assumption
3. $\quad\bullet\quad\bullet\quad\bullet\;p$ --- assumption
4. $\quad\bullet\quad\bullet\quad\bullet\;q\rightarrow r$ --- by $\rightarrow$-elim from 1 and 3
5. $\quad\bullet\quad\bullet\quad\bullet\;r$ --- by $\rightarrow$-elim from 2 and 4
6. $\quad\bullet\quad\bullet\;p\rightarrow r$ --- by $\rightarrow$-Intro from 3 and 5
7. $\quad\bullet\;q\rightarrow \left(p\rightarrow r\right)$ --- by $\rightarrow$-Intro from 2 and 6
8. $\; \left(p\rightarrow\left(q\rightarrow r\right)\right)\rightarrow \left(q\rightarrow \left(p\rightarrow r\right)\right)$ --- by $\rightarrow$-Intro from 1 and 7

Answer 2

$$\dfrac{\quad\dfrac{[p \to (q \to r)]}{\quad\dfrac{\quad\dfrac{[q]}{\quad\dfrac{\dfrac{\dfrac{[p]}{q \to r}{\small\text{MP}}}{r}{\small\text{MP}}}{p \to r}{\small\to\text{I}}\quad}\quad}{q \to (p \to r)}{\small\to\text{I}}\quad}\quad}{(p \to (q \to r)) \to (q \to (p \to r))}{\small\to\text{I}}$$