Show that $((p\Leftrightarrow q)\Leftrightarrow T)$ and $(p\Leftrightarrow (q\Leftrightarrow T))$ are logically equivalent using transformations

Question

I tried this but I'm not sure what to do about the T value:

$$((p\Leftrightarrow q ) \Leftrightarrow T ) \equiv \neg p \Leftrightarrow \neg q \Leftrightarrow T \equiv \neg p \Leftrightarrow \neg (\neg q \Leftrightarrow \neg T) \equiv \neg p \Leftrightarrow (q \Leftrightarrow T)$$

Am I using the rules correctly?

Answer 1

Hint: $\quad r \equiv (r\leftrightarrow \top)$