reserve A,B,C for Ordinal,
  K,L,M,N for Cardinal,
  x,y,y1,y2,z,u for object,X,Y,Z,Z1,Z2 for set,
  n for Nat,
  f,f1,g,h for Function,
  Q,R for Relation;
reserve ff for Cardinal-Function;

theorem Th6:
  Union (X --> Y) c= Y
proof
  let x be object;
  assume x in Union (X --> Y);
  then consider Z such that
A1: x in Z and
A2: Z in rng (X --> Y) by TARSKI:def 4;
  ex z being object st z in dom (X --> Y) & Z = (X --> Y).z
by A2,FUNCT_1:def 3;
  hence thesis by A1,FUNCOP_1:7;
end;
