
theorem Th3:
  for V being 1-sorted, X,Y being Subset of V holds X meets Y iff
  ex v being Element of V st v in X & v in Y
proof
  let V be 1-sorted, X,Y be Subset of V;
  X meets Y implies ex v being Element of V st v in X & v in Y
  proof
    assume X meets Y;
    then consider z being object such that
A1: z in X and
A2: z in Y by XBOOLE_0:3;
    reconsider v = z as Element of V by A1;
    take v;
    thus thesis by A1,A2;
  end;
  hence thesis by XBOOLE_0:3;
end;
