reserve x,A,B,X,X9,Y,Y9,Z,V for set;

theorem Th49:
  X /\ (Y \ Z) = (X /\ Y) \ Z
proof
  now
    let x be object;
    x in X & x in Y & not x in Z iff x in X & x in Y & not x in Z;
    then x in X & x in (Y \ Z) iff x in (X /\ Y) & not x in Z by XBOOLE_0:def 4
,def 5;
    hence x in X /\ (Y \ Z) iff x in (X /\ Y) \ Z by XBOOLE_0:def 4,def 5;
  end;
  hence thesis by TARSKI:2;
end;
