
theorem Th2:
  for X being set, F being Subset-Family of X st F c= Fin X holds
  meet F in Fin X
proof
  let X be set, F be Subset-Family of X such that
A1: F c= Fin X;
  per cases;
  suppose
    F = {};
    hence thesis by FINSUB_1:7,SETFAM_1:1;
  end;
  suppose
    F <> {};
    then consider A being object such that
A2: A in F by XBOOLE_0:def 1;
    reconsider A as set by TARSKI:1;
    meet F c= A by A2,SETFAM_1:3;
    hence thesis by A1,A2,Th1;
  end;
end;
