This is an example solution I am reading but I can't understand the 3rd transformation.

I understand changing the LHS to

< ---a (this)

using set diff representation

(The notes I am reading use this notation where sometimes the intersection operator is "big", does it have an alternate meaning when it is big, or simply a typo?)

If it is just a typo, then I needn't worry about it.

but the next step I don't understand:

(to this) b --->

the notes claim this is using distributivity,

but I can't see how they arrive at that equation using this rule

<-- this I understand,

but I can;t see how they went from a to b