reserve x,y,z,X,Y for set;
reserve X,Y for non empty set,
  f for Function of X,Y;

theorem Th8:
  for X being set for B being Element of Fin X for A being set st
  A c= B holds A is Element of Fin X
proof
  let X be set, B be Element of Fin X;
  let A be set such that
A1: A c= B;
  B c= X by FINSUB_1:def 5;
  then A c= X by A1;
  hence thesis by A1,FINSUB_1:def 5;
end;
