I use my private mobile phone for my job as a sub contractor, how do I prove I use it for my employment? Detailed info or bank statement showing proof of payment

proof of payment does not prove business but only the amount paid.  if you're audited, unless the amount appears unreasonable the agent is unlikely to ask anything about the cell phone except to see the bills to prove the amount.  generally, an agent will accept your oral statement that you use it x% for business.  so keep the bills  - you should only be deducting the business portion. so if you use it 100% for business deduct 100%. if 90% then 90% of the total payments.   

I would at least save the bills as pdf files.  Then only print them if you need to.