reserve p,q,x,x1,x2,y,y1,y2,z,z1,z2 for set;
reserve A,B,V,X,X1,X2,Y,Y1,Y2,Z for set;
reserve C,C1,C2,D,D1,D2 for non empty set;

theorem
  for A being Subset of Y st x in A holds incl(A).x in Y
proof
  let A be Subset of Y such that
A1: x in A;
  dom incl A = A & rng incl A = A;
  then incl(A).x in A by A1,FUNCT_1:def 3;
  hence thesis;
end;
