Prove the validity of the argument below by using logic laws. State the used laws. Show all logical steps.

Given:

$1.$ A v B

$2.$ B $-->($ C $<--->$ D$)$

$3.$ ~B v D

$4.$ C $-->($~H v G$)$

$5.$ H $-->($ A v D$)$

Therefore: H $-->$G