let K, M, N be Cardinal; exp K,(M *` N) = exp (exp K,M),N
A1:
Funcs M,K, card (Funcs M,K) are_equipotent
by CARD_1:def 5;
( [:M,N:],M *` N are_equipotent & [:N,M:],[:M,N:] are_equipotent )
by Lm2, CARD_1:def 5;
then
[:N,M:],M *` N are_equipotent
by WELLORD2:22;
hence exp K,(M *` N) =
card (Funcs [:N,M:],K)
by FUNCT_5:67
.=
card (Funcs N,(Funcs M,K))
by FUNCT_5:70
.=
exp (exp K,M),N
by A1, FUNCT_5:67
;
verum