
theorem Th37:
  for P being Element of ProjectiveSpace TOP-REAL 3 holds
  P is non zero_proj1 or P is non zero_proj2 or P is non zero_proj3
  proof
    let P be Element of ProjectiveSpace TOP-REAL 3;
    assume that
A1: P is zero_proj1 and
A2: P is zero_proj2 and
A3: P is zero_proj3;
    consider u be Element of TOP-REAL 3 such that
A4: u is not zero and
A5: Dir u = P by ANPROJ_1:26;
    reconsider u as non zero Element of TOP-REAL 3 by A4;
    u`1 = 0 & u`2 = 0 & u`3 = 0 by A1,A2,A3,A5;
    hence thesis by EUCLID_5:3,4;
  end;
