reserve x,y,y1,y2,z,a,b for object, X,Y,Z,V1,V2 for set,
  f,g,h,h9,f1,f2 for Function,
  i for Nat,
  P for Permutation of X,
  D,D1,D2,D3 for non empty set,
  d1 for Element of D1,
  d2 for Element of D2,
  d3 for Element of D3;

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;
