Multiple solutions for {↓} ⊢ (p → r) → r

Question

Are both of these correct?

Teacher's solution

{↓} ⊢ (p → r) → r

{↓ , (p → r)} ⊢ r

1 ((p → ↓) → ↓) → p Ax3 F/p

2 ↓ → ((p → ↓) → ↓) Ax2 F/↓ G/(p → ↓)

3 ↓ ∈ Σ

4 ((p → ↓) → ↓) MP 2,3

5 p MP 1,4

6 p → r ∈ Σ

7 r MP 5,6

My solution

{↓} ⊢ (p → r) → r

{↓ , (p → r)} ⊢ r

1 ((r → ↓) → ↓) → r Ax3 F/r

2 ↓ → ((r → ↓) → ↓) Ax2 F/↓ G/(r → ↓)

3 ↓ ∈ Σ

4 ((r → ↓) → ↓) MP 2,3

5 r MP 1,4

Answer 1

Both derivations seem correct to me. It might seem strange to you that you didn't need to use $(p \to r)$ to arrive at the right answer, but when $\bot$ is a hypothesis, everything is easy to prove!

In fact, you've essentially discarded the $p \to r$ and proved the principle of explosion $\bot \to r$.