First, I would be slightly careful with the notation...

In logic, the symbol for "implies" is generally . We use on the "metamathematical" level; i.e., when we want to talk ABOUT formulas such as these. A subtle distinction, but nonetheless important...

Anyway, to prove that and are really the "same thing", I would simply construct a truth table. Make all possible combinations of T and F for each of the two "statements" and, for each, use the rules for the if...then connective to find the truth values of the two statements. If you can prove that the two have the same exact truth table, then you are done.