Question ? Crusader Set bonus and Items !

[Jumpinbuddah420]

The Set "Seeker Of the Light" Give a set bonus Saying : Every Use of Blessed hammer that hits an enemy reduces the cooldown of falling sword and provoke by 1 sec
and there is a belt "Blessed of Haull" That makes your skill "Justice" Spawn a blessed hammer when it hits an enemy

I wanted to know if the hammers that spawn will count with the set bonus and reduce cooldown.