A.T. Robertson Commentary 1 Peter 1:16

"because it is written, Ye shall be holy; for I am holy." — 1 Peter 1:16 (ASV)

Because it is written (διοτ γεγραπτα). "Because (διοτ stronger than οτ below) it stands written" (regular formula for O.T. quotation, perfect passive indicative of γραφω). The quotation is from Le 11:44; 19:2; 20:7. Reenforced by Jesus in Mt 5:48. The future εσεσθε here is volitive like an imperative.