reserve u,v,x,x1,x2,y,y1,y2,z,p,a for object,
        A,B,X,X1,X2,X3,X4,Y,Y1,Y2,Z,N,M for set;
reserve e for object, X,X1,X2,Y1,Y2 for set;

theorem
  for a,b,c,X being set st a in X & b in X & c in X holds {a,b,c} c= X
proof
  let a,b,c,X be set;
  assume a in X & b in X & c in X;
  then {a,b} c= X & {c} c= X by Lm1,Th31;
  then {a,b} \/ {c} c= X by XBOOLE_1:8;
  hence thesis by ENUMSET1:3;
end;
