How can I refinance from FHA to a conventional loan with little or no money down?

Just over 6 months ago, we bought a bank owned property. We've put at least 15 grand into fixing it up. I was told that we can switch to conventional with an appraisal that shows our property is worth 20% more as we don't have cash for closing. Would we not have to pay mortgage insurance if we went conventional and why? I need a little guidance with this. Thanks!