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?

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