let C, A be Ordinal; :: thesis: ( 1 in C implies exp C,A in exp C,(succ A) )
assume A1:
1 in C
; :: thesis: exp C,A in exp C,(succ A)
then
( exp C,A <> {} & 1 *^ (exp C,A) = exp C,A )
by Th22, ORDINAL2:56;
then
( exp C,(succ A) = C *^ (exp C,A) & exp C,A in C *^ (exp C,A) )
by A1, ORDINAL2:57, ORDINAL2:61;
hence
exp C,A in exp C,(succ A)
; :: thesis: verum