On the Relationship Between ID^_

We show that the theory ATR₀ is equivalent to a second-order generalization of the theory $\widehat{ID}_{<\omega}$. As a result, ATR₀ is conservative over $\widehat{ID}_{<\omega}$ for arithmetic sentences, though proofs in ATR₀ can be much shorter than their $\widehat{ID}_{<\omega}$ counterparts.