Alon,
I usually use the function Equivalent together with TautologyQ to test if two logical expressions are equivalent, like this:
(* Let us prove that ((A OR B) => C) <=> (A => C) AND (B => C) *)
Equivalent[Implies[Or[A,B],C], And[Implies[A,C],Implies[B,C]]]//TautologyQ
Now, if you substitute your own expression instead of these two simple ones shown above, then it should work. Note that this is for Mathematica and not for Wolfram Alpha (I don't know if Wolfram Alpha understands the same syntax or not).
