Dr.Shirley P.Thrasher;57;of Detroit;Mich.;and formerly of Arnold City;Belle Vernon died Monday;Oct.17;1994 after a very short illness.  Born in Arnold City on April 4;1937;she was a daughter of the late Weldon and Cora Dupree Thrasher.  She was an attorney in New York and a professor of sociology at Wayne State University in Detroit;Mich.  A graduate of Bellmar High School with the clas of 1955; she went on to receive a B.S.degree in sociology from Blackburn College in 1955;a master degree from Yesinva University in New York in 1979 and a doctorate from Hunter College in sociology in 1988.  Survivors include a son;David Annexstein of Berkley;Calif.;a daughter;Leslie Annestein of Arlington;Va.;four sisters;Sylvia Joyner of Las Vegas;Nev.;Sonia Parker and Millicent Sellers;both of Arnold City;and Kathy Wilson of Rochester;N.Y.;and a grandmother;Aggie Dupree of Belle Vernon.  In addition to her parents;she was preceded in death by three brothers;Stephen in 1976 and Richard and Melvin Thrasher in 1990.  Friends will be received Friday from 2 to 4 and 7 to 9 p.m.in the Howard W;McCrory Funeral Home;Main Street;Fayette Citry;and Saturday from 11 a.m.to 1 p.m.in the First Christian Church of Wick Haven.