Could I convert my FHA loan into conventional using the equity?

Could I convert my FHA loan into conventional using the equity?
Added (1). I started an FHA loan at $400K. I am 5 years in and owe $350K; my house is worth $550K. I am currently paying $175 PMI. Could I refinance my house for the amount I owe ($350K) and use the equity to alleviate the required down payment for a conventional loan so that I don't have to pay the PMI? Basically, I want to convert my FHA into conventional loan without money out of my pocket by financing the same mortgage balance (no less/no more) at possibly a lower interest rate. I currently have 4.5.

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