Prove that $(p \to q) \to (\neg q \to \neg p)$ is a tautology using the law of logical equivalence I'm new to discrete maths and I have been trying to solve this:

Decide whether $$(p \to q) \to (\neg q \to \neg p)$$ is a tautology or not by using the law of logical equivalence

I have constructed the truth table and concluded that it is indeed a tautology. However, I am having difficulty proving it using the law of logical equivalence.
I can only realize that I can use $$(p \to q ) \equiv (\neg p \lor q)$$ but after that I have no idea how to continue. Any help would be appreciated.

The following line of reasoning may help:
$\qquad\begin{align}
(p\to q)\to(\neg q\to\neg p)&\equiv\neg(\neg p\lor q)\lor(q\lor\neg p)&&\text{material implication}\\[1em]
&\equiv\neg(\neg p\lor q)\lor(\neg p\lor q)&&\text{commutativity}\\[1em]
&\equiv \neg M\lor M&&{M:\neg p\lor q}\\[1em]
&\equiv \mathbf{T}&&\text{negation law}
\end{align}$
Is the above clear? It makes minimal use of other logical equivalences.
