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(K,M*`N) = exp(exp(K,M),N)
proof
A1: Funcs(M,K),card Funcs(M,K) are_equipotent by CARD_1:def 2;
  [:M,N:],M*`N are_equipotent & [:N,M:],[:M,N:] are_equipotent by Lm2,
CARD_1:def 2;
  then [:N,M:],M*`N are_equipotent by WELLORD2:15;
  hence exp(K,M*`N) = card Funcs([:N,M:],K) by FUNCT_5:60
    .= card Funcs(N,Funcs(M,K)) by FUNCT_5:63
    .= exp(exp(K,M),N) by A1,FUNCT_5:60;
end;
