diff --git a/explorer/data/prelude.carbon b/explorer/data/prelude.carbon
index 4ac5a0fb23b3..1a6baaef1775 100644
--- a/explorer/data/prelude.carbon
+++ b/explorer/data/prelude.carbon
@@ -83,6 +83,15 @@ impl forall [T2:! Type, U2:! Type, T1:! EqWith(T2), U1:! EqWith(U2)]
     }
 }
 
+impl bool as EqWith(Self) {
+  fn Equal[me: Self](other: Self) -> bool {
+    return if me then other else not other;
+  }
+  fn NotEqual[me: Self](other: Self) -> bool {
+    return if me then not other else other;
+  }
+}
+
 impl i32 as EqWith(Self) {
   fn Equal[me: Self](other: Self) -> bool {
     return __intrinsic_int_eq(me, other);
@@ -437,16 +446,16 @@ choice OptionalElement(T:! Type) {
   Element(T)
 }
 
-class Optional(T:! Type){
-  fn CreateEmpty() -> Optional(T){
-    return { .element = OptionalElement(T).None() };
+class Optional(T:! Type) {
+  fn CreateEmpty() -> Optional(T) {
+    return {.element = OptionalElement(T).None()};
   }
-  fn Create(value: T ) -> Optional(T){
-    return { .element = OptionalElement(T).Element(value) };
+  fn Create(value: T) -> Optional(T) {
+    return {.element = OptionalElement(T).Element(value)};
   }
 
   fn HasValue[me: Self]() -> bool {
-    match(me.element){
+    match(me.element) {
       case OptionalElement(T).None() => { return false; }
     }
     return true;
@@ -454,8 +463,8 @@ class Optional(T:! Type){
 
   fn Get[me: Self]() -> T {
     var y: T;
-    match(me.element){
-      case OptionalElement(T).Element(x: T ) =>{
+    match(me.element) {
+      case OptionalElement(T).Element(x: T) => {
         return x;
       }
     }
diff --git a/explorer/testdata/comparison/builtin_equality.carbon b/explorer/testdata/comparison/builtin_equality.carbon
index 4bcc51f60c00..601f5da50bce 100644
--- a/explorer/testdata/comparison/builtin_equality.carbon
+++ b/explorer/testdata/comparison/builtin_equality.carbon
@@ -7,18 +7,54 @@
 // RUN: %{explorer} --parser_debug --trace_file=- %s 2>&1 | \
 // RUN:   %{FileCheck} --match-full-lines --allow-unused-prefixes %s
 // AUTOUPDATE: %{explorer} %s
-// CHECK: strings equal: 0
-// CHECK: ints equal: 1
-// CHECK: strings not eq: 1
-// CHECK: ints not eq: 0
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: bool: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: string: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
+// CHECK: int: 1
 // CHECK: result: 0
 
 package ExplorerTest api;
 
+fn CompareEqualValues[T:! EqWith(.Self)](format: String, a: T, b: T) {
+  Print(format, if a == b then 1 else 0);
+  Print(format, if a != b then 0 else 1);
+}
+
+fn CompareDifferentValues[T:! EqWith(.Self)](format: String, a: T, b: T) {
+  Print(format, if a == b then 0 else 1);
+  Print(format, if a != b then 1 else 0);
+}
+
+fn CompareAll[T:! EqWith(.Self)](format: String, a: T, b: T) {
+  CompareEqualValues(format, a, a);
+  CompareEqualValues(format, b, b);
+  CompareDifferentValues(format, a, b);
+  CompareDifferentValues(format, b, a);
+}
+
 fn Main() -> i32 {
-  Print("strings equal: {0}", if "hello" == "world" then 1 else 0);
-  Print("ints equal: {0}", if 1 == 1 then 1 else 0);
-  Print("strings not eq: {0}", if "hello" != "world" then 1 else 0);
-  Print("ints not eq: {0}", if 1 != 1 then 1 else 0);
+  CompareAll("bool: {0}", false, true);
+  CompareAll("string: {0}", "hello", "world");
+  CompareAll("int: {0}", 1, 2);
   return 0;
 }