let V be RealLinearSpace; :: thesis: for v being VECTOR of V st v + v = 0. V holds
v = 0. V
let v be VECTOR of V; :: thesis: ( v + v = 0. V implies v = 0. V )
assume v + v = 0. V ; :: thesis: v = 0. V
then v = - v by Def13;
hence v = 0. V by Th33; :: thesis: verum