diff --git a/laws/src/main/scala/cats/laws/DistributiveLaws.scala b/laws/src/main/scala/cats/laws/DistributiveLaws.scala
index db45442101..1df311b445 100644
--- a/laws/src/main/scala/cats/laws/DistributiveLaws.scala
+++ b/laws/src/main/scala/cats/laws/DistributiveLaws.scala
@@ -8,6 +8,10 @@ import cats.syntax.distributive._
 trait DistributiveLaws[F[_]] extends FunctorLaws[F] {
   implicit override def F: Distributive[F]
 
+  def distributeIdentity[A, B](fa: F[A], f: A => B): IsEq[F[B]] = {
+    fa.distribute[Id, B](f) <-> F.map(fa)(f)
+  }
+
   def cosequenceIdentity[A](fa: F[A]): IsEq[F[A]] = {
     F.cosequence[Id, A](fa) <-> fa
   }
diff --git a/laws/src/main/scala/cats/laws/discipline/DistributiveTests.scala b/laws/src/main/scala/cats/laws/discipline/DistributiveTests.scala
index 7d25a5b5a7..c4a54479d8 100644
--- a/laws/src/main/scala/cats/laws/discipline/DistributiveTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/DistributiveTests.scala
@@ -18,6 +18,7 @@ trait DistributiveTests[F[_]] extends FunctorTests[F] {
     CogenB: Cogen[B],
     CogenC: Cogen[C],
     EqFA: Eq[F[A]],
+    EqFB: Eq[F[B]],
     EqFC: Eq[F[C]],
     EqA: Eq[A],
     EqFYXC: Eq[F[Y[X[C]]]],
@@ -29,6 +30,7 @@ trait DistributiveTests[F[_]] extends FunctorTests[F] {
       def bases: Seq[(String, RuleSet)] = Nil
       def parents: Seq[RuleSet] = Seq(functor[A, B, C])
       def props: Seq[(String, Prop)] = Seq(
+        "distributive distribute identity" -> forAll(laws.distributeIdentity[A, B] _),
         "distributive identity" -> forAll(laws.cosequenceIdentity[A] _),
         "distributive composition" -> forAll(laws.composition[A, B, C, X, Y] _),
         "distributive double cosequence identity" -> forAll(laws.cosequenceTwiceIsId[A, Y] _)