Mutually Exclusive Enchantments go onto same Armor Piece

Enchanted my Diamond Chestplate at an Enchanting Table, and got Protection IV and Fire Protection IV on it at the same time. Tried combining it with an enchanted book with Blast Protection IV and it seemed to work too.

Edit: I tested it by trying to put Smite onto my Sharpness Sword, and that is not working, so it seems to be with armor enchantments only.