Final answer:
In The Binding of Isaac: Rebirth, 'Blood Rights' is the item that deals 40 damage to all enemies in a room at the cost of one heart, but causes no damage when used with 'Isaac's Heart'.
Step-by-step explanation:
The item in The Binding of Isaac: Rebirth that takes away one full heart and deals 40 damage to the entire room is Blood Rights. However, when this item is paired with Isaac's Heart, players can use Blood Rights without taking any damage. The synergy between these two items is unique because Isaac's Heart makes Isaac immune to the heart damage that Blood Rights would normally inflict upon use.
Learn more about The Binding of Isaac: Rebirth Items