In last some decades, Fuzzy topology has been extensively used in logic programming. It has been noticed by several researchers that, this theory was applied on various logical program to find more truthful result. The strength of fuzzy mathematics lies in its usefulness and having fruitful applications especially outside mathematics. In this paper, we prove some common fixed point theorem by using E.A. property in fuzzy metric spaces. We prove our results in fuzzy metric spaces in the sense of Kramosil and Michalek [1]. Our result generalize and extend relevant result of Mihet [2] and Vijayaraju [3]. An application of finite families of self mappings is given to support our result.