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

theorem
  X meets Y implies X /\ Y meets Y
proof
  assume X meets Y;
  then consider x being object such that
A1: x in X and
A2: x in Y by XBOOLE_0:3;
  x in X /\ Y by A1,A2,XBOOLE_0:def 4;
  hence thesis by A2,XBOOLE_0:3;
end;
