Hi Nita, no I can't prove that the Thomas Gerren b. abt. 1852, TX had parents living in Bradley Co., TN.
Have you found his birth certificate in Texas? I can't find anything in the Censuses prior to the 1880 Denton Co. Census. The Texas Dept. State Health Services has info about birth certs. See http://www.dshs.state.tx.us/vs/default.shtmhttp://www.dshs.state.tx.us/vs/default.shtm. Successful Searching!