What's the shortcut?
\[ (A \iff B)\iff \neg (A \Rightarrow B)\Rightarrow \neg(B\Rightarrow A) \]
There are two ways to prove if a statement is a tautology:
1. Build a truth table
2. Supposing the statmement is false and concluding a contradiction.
Is the mathematical statement at the top a tautology?