The phrase "proved acceptable" can mean that something has been found to be satisfactory or suitable for a specific purpose. There are several synonyms that can be used in place of this phrase such as "accepted", "validated", "approved", "endorsed" or "acquiesced". A similar synonym is "confirmed", which suggests that something has been verified and acknowledged to be true or valid. Another synonym is "sanctioned", which means that something has been authorized or given official approval. Whatever word you choose, the meaning behind it is that something has met the required standards and has been judged to be acceptable.