reserve x,y for object,X,Y,A,B,C,M for set;
reserve P,Q,R,R1,R2 for Relation;

theorem
  for B1, B2 being Subset-Family of M holds
  Intersect(B1) /\ Intersect(B2) c= Intersect(B1 /\ B2)
proof
  let B1, B2 be Subset-Family of M;
  Intersect(B1 \/ B2) c= Intersect(B1 /\ B2) by SETFAM_1:44,XBOOLE_1:29;
  hence thesis by MSSUBFAM:8;
end;
