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

theorem Th26:
  X c= Y implies X /\ Z c= Y /\ Z
proof
  assume
A1: X c= Y;
  let x be object;
  assume
A2: x in X /\ Z;
  then x in X by XBOOLE_0:def 4;
  then
A3: x in Y by A1;
  x in Z by A2,XBOOLE_0:def 4;
  hence thesis by A3,XBOOLE_0:def 4;
end;
