Heterograms, Palindromes, oh my! (First challenge, please let me know if there are any problems with it.)

A heterogram is a word where no letter of the alphabet occurs more than once, and a palindrome is a phrase that is the same backwards and forwards. 

The challenge here is to write a piece of code that takes in a word (just letters) as input, and outputs whether or not it is a heterogram (truthy/falsy). The catch is that the program must be a palindrome -- reads the same backwards and forwards. Capitalization doesn't matter here, so for the heterogram to be valid it can't have both q and Q, for instance.  No comments are allowed, and you cannot place strings that contain your code (or a significant part of your code) to try to make the palindrome part easy :P

This is code-golf, so shortest code wins. Good luck!

EDIT: Parens, brackets or other symbols that have left and right forms must be reversed approriately for the palindrome part. So (helloolleh) is a palindrome, but (helloolleh( is not. Apparently this is called a convenient palindrome.

EDIT 2: You won't get any empty input, input with multiple words or input with characters other than letters. So don't worry about that :)
Pyth, 17 bytes
 Z.{rzZ.q.Zzr}.Z 

Try it online here.
The leading space is necessary. I have counted it and the trailing space in the byte count.
Here's the breakdown:
     z            z is initialized to the input
    r Z           Z is initialized to 0, and r(string)0 converts the string to lowercase
  .{              .{ is pyth's builtin uniqueness test
       .q         .q terminates the program
         .Zzr}    This is just the program mirrored
              .Z  . requires a number to immediately follow it
                  If left blank the parser would throw an error
 Z                This is just mirrored from the end
                  The leading space suppresses the automatic printing of this 0
                  The trailing space mirrors the leading space