Blackadar's [K-Theory for operator algebras][1] has it, although the way it is done there is perhaps overkill if this is all you need.  The result is generalized to local $C^*$-algebras, and they show similarity by showing the stronger property of homotopy equivalence.  It is [Proposition 4.6.2][2] on page 23 of the 2nd edition (1998).  ([Proposition 4.3.3][3] shows that homotopy equivalence is stronger.)

The stronger equivalence (but just for $C^*$-algebras) is also shown in the K-theory book by Rørdam et al., [Lemma 11.2.7][4], with a very similar proof.


  [1]: http://books.google.com/books?id=214a1Wri63QC&dq=idempotent+projection+similar&client=firefox-a&source=gbs_navlinks_s
  [2]: http://books.google.com/books?id=214a1Wri63QC&lpg=PA23&dq=idempotent%2520projection%2520similar&client=firefox-a&pg=PA23#v=onepage&q=&f=false
  [3]: http://books.google.com/books?id=214a1Wri63QC&lpg=PA23&dq=idempotent%2520projection%2520similar&client=firefox-a&pg=PA21#v=onepage&q=idempotent%2520projection%2520similar&f=false
  [4]: http://books.google.com/books?id=SMiB8VIB5UIC&lpg=PA192&dq=idempotent%2520projection%2520k-theory&client=firefox-a&pg=PA192#v=onepage&q=&f=false