Using Logic Laws to prove $p \leftrightarrow q \equiv (p\lor q)\to(p \land q)$ I am trying to prove that

$p \leftrightarrow q \equiv (p\lor q)\to(p \land q)$

and am really lost in the steps to solve this.
So far I have:

$p \leftrightarrow q \equiv (p\to q)\land(q\to p) \qquad$|equivalence
   $p \leftrightarrow q\equiv (\neg p\lor q)\land(\neg q\lor p) \qquad$|implication

and I am not sure how to proceed from here. Any advice would be greatly appreciated!
edit:
Thanks to lord farin i now have 

≡ (~p ∨ q) ∧ (q → p)  Implication Law
  ≡ (q → p) ∧ (~p ∨ q)  Commutative Law
  ≡ (q → p ∧ ~p ) ∨ (q → p ∧ q) Distributive Law
  ≡ (~p ∧ q → p) ∨ (q ∧ q → p) Commutative Law

but i am unsure of how to get there still. 

You could write equivalence as $(p \land q) \lor (\lnot p \land \lnot q)$, which gives us, using commutation and implication law, the result you desire.
