Give a reason for each step in the following argument

Question

Give a reason for each step in the following argument to prove the statement for any propositions A, B, and C:

([A → (B ∨C)] ∧¬B ∧¬C) → ¬A

1. A → (B ∨C)
2. ¬B
3. ¬C
4. ¬B ∧¬C
5. ¬(B ∨C)
6. ¬A

What is this problem asking exactly? Am I just describing what's happening? Any help is appreciated

Answer 1

You have to "comment" each line in the proof, specifying if it is a premise or it is derived from previous lines; in this case, what lines and by which rule.

1) $[A → (B ∨ C)] \land \lnot B \land \lnot C$ --- premise

2) $A → (B ∨ C)$ --- from 1) by $\land$-elimination

3) $¬B$ --- from 1) by $\land$-elimination

4) $¬C$ --- from 1) by $\land$-elimintion

4) $¬B ∧ ¬C$ --- from 3) and 4) by $\land$-introuction

5) $\ldots$