What are the stable isotopes of carbon

Write an equational-style proof for the following theorem schema: ⊢ (¬((A ∨ C) ≡ (¬B))) ≡ (A ∨ B ∨ C) ≡ ((A ∨ C) ∧ B)

for this question, is this answer correct:
 

We will prove the theorem schema in two steps:

1. Prove that ¬((A ∨ C) ≡ ¬B) is logically equivalent to (A ∨ B ∨ C).
2. Prove that (A ∨ B ∨ C) is logically equivalent to ((A ∨ C) ∧ B).

Step 1: Prove ¬((A ∨ C) ≡ ¬B) ≡ (A ∨ B ∨ C)

We can rewrite the left-hand side of the equivalence as follows:

¬((A ∨ C) ≡ ¬B)
≡ ¬((A ∨ C) ∧ B) ∧ ¬(¬(A ∨ C) ∧ ¬¬B)  (by definition of ≡)
≡ ¬(A ∨ C) ∨ ¬B ∨ ¬¬(A ∨ C) ∨ B  (by De Morgan's laws)
≡ (A ∨ B ∨ C)  (by double negation and commutativity)

Step 2: Prove (A ∨ B ∨ C) ≡ ((A ∨ C) ∧ B)

We can rewrite the left-hand side of the equivalence as follows:

(A ∨ B ∨ C)
≡ (A ∨ (B ∨ C))  (by associativity)
≡ ((A ∨ C) ∨ B)  (by commutativity)
≡ ((A ∨ C) ∧ B)  (by distributivity)

Use either Hilbert or equational-style proof to prove the theorem schema

⊢(B→C)≡(¬((B∨C)→C))≡(¬((B∧C)∨⊤))

Use either Hilbert or equational-style proof to prove the theorem schema

⊢(B→C)≡(¬((B∨C)→C))≡(¬((B∧C)∨⊤))

Use either Hilbert or equational-style proof to prove the theorem schema

⊢(B→C)≡(¬((B∨C)→C))≡(¬((B∧C)∨⊤))

Write an equational-style proof for the following theorem schema:

⊢(¬((A∨C)≡(¬B)))≡(A∨B∨C)≡((A∨C)∧B)

Write an equational-style proof for the following theorem schema:

⊢(¬((A∨C)≡(¬B)))≡(A∨B∨C)≡((A∨C)∧B)