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

theorem
  X c= Y & Z c= V implies X /\ Z c= Y /\ V
proof
  assume that
A1: X c= Y and
A2: Z c= V;
  let x be object;
  assume
A3: x in X /\ Z;
  then x in Z by XBOOLE_0:def 4;
  then
A4: x in V by A2;
  x in X by A3,XBOOLE_0:def 4;
  then x in Y by A1;
  hence thesis by A4,XBOOLE_0:def 4;
end;
