reserve V for Universe,
  a,b,x,y,z,x9,y9 for Element of V,
  X for Subclass of V,
  o,p,q,r,s,t,u,a1,a2,a3,A,B,C,D for set,
  K,L,M for Ordinal,
  n for Element of omega,
  fs for finite Subset of omega,
  e,g,h for Function,
  E for non empty set,
  f for Function of VAR,E,
  k,k1 for Element of NAT,
  v1,v2,v3 for Element of VAR,
  H,H9 for ZF-formula;

theorem Th5:
  X is closed_wrt_A1-A7 & A in X & B in X implies A/\B in X
proof
  assume that
A1: X is closed_wrt_A1-A7 & A in X and
A2: B in X;
  A\B in X by A1,A2,Th4;
  then A\(A\B) in X by A1,Th4;
  hence thesis by XBOOLE_1:48;
end;
