The other three pieces of Ornate Mithril plate are learned from this NPC:

https://vanillawowdb.com/?npc=7802 https://vanillawowdb.com/?npc=7802

Since you technically need his recipes to complete these quests, it's fair to call his quests a prereq.

Nevertheless, carefully consider the cost of all three quests in this line and check the AH for which path is cheaper (buying the armor vs making the armor yourself)

All told you need:

Mithril Coif x2
Ornate Mithril Shoulder
Heavy Mithril Breastplate x2
Ornate Mithril Gloves
Heavy Mithril Boots x2
Ornate Mithril Pants

To make all the armor yourself you need the total ingredients listed here:

Mithril Bar x106
Truesilver Bar x 3
Mageweave Cloth x 18
Thick Leather x 14
Solid Grinding Stone x 3

I strongly suggest you do the math for your realm's AH prices. Often it is significantly cheaper to buy the armor pieces than to make it yourself.