$(5$ points$)$ Show that the left hand side is logically equivalent to the right hand side through transitivity of logical equivalence. Write each step $(1/2$ pt$.$ each$)$ together with the corresponding logical law $($that is$,$ the notable propositional or predicative logical equivalence$)$ used $(1/2$ pt$.$ each$).$

$($a$)$ Prove $$y$$x$($F $($x$)->$G$($y$))$x$$y$($F $($x$)$ G$($y$))$