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(K,M)*`exp(K,N)
proof
A1: [:M,{0}:] misses [:N,{1}:] by ZFMISC_1:108;
  [:M,{0}:],M are_equipotent by CARD_1:69;
  then
A2: Funcs([:M,{0}:],K),Funcs(M,K) are_equipotent by FUNCT_5:60;
  [:N,{1}:],N are_equipotent by CARD_1:69;
  then
A3: Funcs([:N,{1}:],K),Funcs(N,K) are_equipotent by FUNCT_5:60;
  M+`N,[:M,{0}:] \/ [:N,{1}:] are_equipotent by Th9;
  hence exp(K,M+`N) = card Funcs([:M,{0}:] \/ [:N,{1}:],K) by FUNCT_5:60
    .= card [:Funcs([:M,{0}:],K),Funcs([:N,{1}:],K):] by A1,FUNCT_5:62
    .= card [:Funcs(M,K),Funcs(N,K):] by A2,A3,Th7
    .= exp(K,M)*`exp(K,N) by Th6;
end;
