theorem Th23:
  X <> {} implies Union (X --> Y) = Y & meet (X --> Y) = Y
proof
  assume X <> {};
  then
A1: rng (X --> Y) = {Y} by FUNCOP_1:8;
  then union rng (X --> Y) = Y by ZFMISC_1:25;
  hence thesis by A1,CARD_3:def 4,SETFAM_1:10;
end;
