Natural deduction proof unsure if correct

Question

I'm unsure if this method of natural deduction is correct.

To prove: $P \vee F,\; \neg T \mathbin\rightarrow \neg P,\; T \mathbin\rightarrow B,\; \neg F \;\vDash\; B$

Proof:

1. $P \vee F$ (Data)
2. $\neg T \mathbin\rightarrow \neg P$ (Data)
3. $T \mathbin\rightarrow B$ (Data)
4. $\neg F$ (Data)
5. $\neg T \mathbin\rightarrow P$ (subcomp box)
   1. $\neg T$ (Assume P)
   2. $P$ (from 1,4,($\vee$E2))
6. $T$ from (2,5,($\neg$E))
7. $B$ from (3,6,($\mathbin\rightarrow$E))

Reference picture

I tried to solve using this method; I'm not sure if it is correct.