theorem
  for R being Ring,
      V being LeftMod of R,
      v1,v2 being Vector of V holds
  R is non degenerated & {v1,v2} is linearly-independent implies
    v1 <> 0.V & v2 <> 0.V
proof
  let R be Ring,
      V be LeftMod of R,
      v1,v2 be Vector of V;
A1: v1 in {v1,v2} & v2 in {v1,v2} by TARSKI:def 2;
  assume R is non degenerated & {v1,v2} is linearly-independent;
  hence thesis by A1,Th2;
end;
