What's the shortcut?

Logic Level 2

$(A \iff B)\iff \neg (A \Rightarrow B)\Rightarrow \neg(B\Rightarrow A)$

Two possible ways to prove if a statement is a tautology are these:
1. Build a truth table.
2. Supposing the statement is false and concluding a contradiction or not.

Is the mathematical statement at the top a tautology?