“Don’t be irreplaceable; if you can’t be replaced, you can’t be promoted” is a popular saying on many websites that list office proverbs and jokes. “Don’t be indispensable. If you can’t be replaced, you can’t be promoted” has been cited in print since at least October 1971 and is of unknown authorship. “Indispensable” was replaced by “irreplaceable” by at least 1981.
 
 
27 October 1971,

(Kittanning, PA), “Briefly Noted,” pg. 6, col. 1:
Don’t be indispensable. If you can’t be replaced, you can’t be promoted.
 
6 November 1971, Cedar Rapids (IA) Gazette, “Today’s Chuckle,” pg. 1, col. 8:
Don’t be indispensable. If you can’t be replaced, you can’t be promoted.
 
31 May 1977, Seattle (WA) Times, “I’m not one who’s cuckoo over the flu” by Walt Evans, pg. A10, col. 1:
Mack McGinnis passes along a little advice for you graduates: “Don’t be indispensable—if you can’t be replaced, you can’t be promoted.” Never though of it that way.
 
30 January 1981, Seattle (WA) Times, “Why things aren’t the way they should be” by Paul Dickson (from his book, The Official Explanations), pg. C1, col. 4:
Upward-Mobility Rule.
Don’t be irreplaceable. If you can’t be replaced, you can’t be promoted.
 
Google Books
Thriving:
The journey to success in the business world
By Jania L. Bailey
Louisville, KY: Letters Etcetera
1997
Pg. 72:
“Don’t be irreplaceable. If you can’t be replaced, you can’t be promoted.”
Anonymous
 
Google Books
Effective Management of Student Employment:
Organizing for Student Employment in Academic Libraries
By David Allen Baldwin, Frances C. Wilkinson and Daniel C. Barkley
Englewood, CO: Libraries Unlimited, Inc.
2000
Pg. 50:
10. Don’t become indispensable. If you are indispensable, you can’t be replaced or promoted. If you are indispensable, you are not delegating properly, not interacting with others, and not training anyone to fill in during your absences.
 
Google Books
Murphy’s Law (26th Anniversary Edition)
By Arthur Bloch
New York, NY: Perigee
2003
Pg. 49:
Chapman’s Law
Don’t be irreplaceable. If you can’t be replaced, you can’t be promoted.
   
Google Books
The 101 Greatest Business Principles Of All Time
By Leslie Pockell and Adrienne Avila
Pg. 112:
Don’t be irreplaceable — if you can’t be replaced, you can’t be promoted. ♢ Dilbert (Scott Adams)
   
Google Books
Oxymorons and Other Contradictions
By Wrong Way
Bloomington, IN: AuthorHouse
2005
Pg. 19:
Don’t be irreplaceable; if you can’t be replaced, you can’t be promoted.
 
Google Books
Jokes, Quotes, And Other Assorted Things
By Stephen Motway
Xlibris Corporation
2011
Pg. 222:
Don’t be irreplaceable; if you can’t be replaced, you can’t be promoted.