diff --git a/src/libcore/cmp.rs b/src/libcore/cmp.rs
index 86f28a957cd2c..d43a5c1032ce0 100644
--- a/src/libcore/cmp.rs
+++ b/src/libcore/cmp.rs
@@ -91,6 +91,8 @@ use self::Ordering::*;
 /// For example, let's tweak our previous code a bit:
 ///
 /// ```
+/// // The derive implements <BookFormat> == <BookFormat> comparisons
+/// #[derive(PartialEq)]
 /// enum BookFormat {
 ///     Paperback,
 ///     Hardback,
@@ -102,31 +104,34 @@ use self::Ordering::*;
 ///     format: BookFormat,
 /// }
 ///
+/// // Implement <Book> == <BookFormat> comparisons
 /// impl PartialEq<BookFormat> for Book {
 ///     fn eq(&self, other: &BookFormat) -> bool {
-///         match (&self.format, other) {
-///            (BookFormat::Paperback, BookFormat::Paperback) => true,
-///            (BookFormat::Hardback,  BookFormat::Hardback)  => true,
-///            (BookFormat::Ebook,     BookFormat::Ebook)     => true,
-///            (_, _) => false,
-///         }
+///         self.format == *other
+///     }
+/// }
+///
+/// // Implement <BookFormat> == <Book> comparisons
+/// impl PartialEq<Book> for BookFormat {
+///     fn eq(&self, other: &Book) -> bool {
+///         *self == other.format
 ///     }
 /// }
 ///
 /// let b1 = Book { isbn: 3, format: BookFormat::Paperback };
 ///
 /// assert!(b1 == BookFormat::Paperback);
-/// assert!(b1 != BookFormat::Ebook);
+/// assert!(BookFormat::Ebook != b1);
 /// ```
 ///
 /// By changing `impl PartialEq for Book` to `impl PartialEq<BookFormat> for Book`,
-/// we've changed what type we can use on the right side of the `==` operator.
-/// This lets us use it in the `assert!` statements at the bottom.
+/// we allow `BookFormat`s to be compared with `Book`s.
 ///
 /// You can also combine these implementations to let the `==` operator work with
 /// two different types:
 ///
 /// ```
+/// #[derive(PartialEq)]
 /// enum BookFormat {
 ///     Paperback,
 ///     Hardback,
@@ -140,12 +145,13 @@ use self::Ordering::*;
 ///
 /// impl PartialEq<BookFormat> for Book {
 ///     fn eq(&self, other: &BookFormat) -> bool {
-///         match (&self.format, other) {
-///            (&BookFormat::Paperback, &BookFormat::Paperback) => true,
-///            (&BookFormat::Hardback,  &BookFormat::Hardback)  => true,
-///            (&BookFormat::Ebook,     &BookFormat::Ebook)     => true,
-///            (_, _) => false,
-///         }
+///         self.format == *other
+///     }
+/// }
+///
+/// impl PartialEq<Book> for BookFormat {
+///     fn eq(&self, other: &Book) -> bool {
+///         *self == other.format
 ///     }
 /// }
 ///
@@ -159,7 +165,7 @@ use self::Ordering::*;
 /// let b2 = Book { isbn: 3, format: BookFormat::Ebook };
 ///
 /// assert!(b1 == BookFormat::Paperback);
-/// assert!(b1 != BookFormat::Ebook);
+/// assert!(BookFormat::Ebook != b1);
 /// assert!(b1 == b2);
 /// ```
 ///