reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;

theorem
  exp(2,card X) = card bool X
proof
  card card X = card X & card 2 = card {{},1} by CARD_1:50;
  hence exp(2,card X) = card Funcs(X,{{},1}) by FUNCT_5:61
    .= card bool X by FUNCT_5:65;
end;
