let R be Ring; :: thesis: for V being LeftMod of R
for v being Element of V holds (ZeroLC V) . v = 0. R
let V be LeftMod of R; :: thesis: for v being Element of V holds (ZeroLC V) . v = 0. R
let v be Element of V; :: thesis: (ZeroLC V) . v = 0. R
( Carrier (ZeroLC V) = {} & not v in {} ) by VECTSP_6:def 3;
hence (ZeroLC V) . v = 0. R ; :: thesis: verum