
theorem
  for X be set, S be set st S is SigmaField of X holds S is SigmaRing of X
proof
   let X be set, S be set;
   assume A1: S is SigmaField of X; then
   for F be SetSequence of X st rng F c= S holds Union F in S by PROB_4:4;
   hence S is SigmaRing of X by A1,DefSigmaRing;
end;
