
theorem
  for R being domRing holds {0.R} is prime
proof
  let R be domRing;
  not 1_R in {0.R} by TARSKI:def 1;
  hence {0.R} is proper by IDEAL_1:19;
  let a, b be Element of R;
  assume a*b in {0.R};
  then a*b = 0.R by TARSKI:def 1;
  then a = 0.R or b = 0.R by VECTSP_2:def 1;
  hence thesis by TARSKI:def 1;
end;
