let R be Ring; :: thesis: for V being LeftMod of R holds {} the carrier of V is linearly-independent
let V be LeftMod of R; :: thesis: {} the carrier of V is linearly-independent
let l be Linear_Combination of {} the carrier of V; :: according to LMOD_5:def 1 :: thesis: ( Sum l = 0. V implies Carrier l = {} )
Carrier l c= {} by VECTSP_6:def 4;
hence ( Sum l = 0. V implies Carrier l = {} ) ; :: thesis: verum