I need to use a Hilbert style proof and deduction theorem to solve this, however, I am not allowed to use post theorem.

Question

Picture containing question

I need help trying to solve this. A short explanation would be greatly appreciated.

Answer 1

1) $A \equiv (B \equiv C)$ --- premise

2) $A$ --- assumed [a]

3) $B \equiv C$ --- from 1) and 2) by Equanimity rule.

4) $B$ --- assumed [b]

5) $C$ --- from 3) and 4) by Equanimity.

6) $A \to (B \to C)$ --- from 2), 4) and 5) by Deduction Theorem twice, dicarding assumptions [a] and [b],