reserve V for non empty set,
  A,B,A9,B9 for Element of V;
reserve f,f9 for Element of Funcs(V);
reserve m,m1,m2,m3,m9 for Element of Maps V;
reserve a,b for Object of Ens(V);
reserve f,g,f1,f2 for Morphism of Ens(V);

theorem Th26:
  Hom(a,b) = Maps(@a,@b)
proof
  now
    let x be object;
    thus x in Hom(a,b) implies x in Maps(@a,@b)
    proof
      assume
A1:   x in Hom(a,b);
      then reconsider f = x as Morphism of Ens(V);
      cod(f) = b by A1,CAT_1:1;
      then
A2:   cod(@f) = @b by Def10;
      dom(f) = a by A1,CAT_1:1;
      then dom(@f) = @a by Def9;
      hence thesis by A2,Th19;
    end;
    assume
A3: x in Maps(@a,@b);
    Maps(@a,@b) c= Maps V by Th17;
    then reconsider m = x as Element of Maps V by A3;
    cod(m) = @b by A3,Th19;
    then
A4: cod(@m) = b by Def10;
    dom(m) = @a by A3,Th19;
    then dom(@m) = a by Def9;
    hence x in Hom(a,b) by A4;
  end;
  hence thesis by TARSKI:2;
end;
