Description: Ordinal exponentiation with a successor exponent. Definition 8.30 of TakeutiZaring p. 67. (Contributed by NM, 31-Dec-2004) (Revised by Mario Carneiro, 8-Sep-2013)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | oesuc | |- ( ( A e. On /\ B e. On ) -> ( A ^o suc B ) = ( ( A ^o B ) .o A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | limon | |- Lim On |
|
| 2 | rdgsuc | |- ( B e. On -> ( rec ( ( x e. _V |-> ( x .o A ) ) , 1o ) ` suc B ) = ( ( x e. _V |-> ( x .o A ) ) ` ( rec ( ( x e. _V |-> ( x .o A ) ) , 1o ) ` B ) ) ) |
|
| 3 | 1 2 | oesuclem | |- ( ( A e. On /\ B e. On ) -> ( A ^o suc B ) = ( ( A ^o B ) .o A ) ) |