Description: The collection of ordinal numbers in the power set of an ordinal number is its successor. (Contributed by NM, 19-Oct-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | onpwsuc | |- ( A e. On -> ( ~P A i^i On ) = suc A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni | |- ( A e. On -> Ord A ) |
|
2 | ordpwsuc | |- ( Ord A -> ( ~P A i^i On ) = suc A ) |
|
3 | 1 2 | syl | |- ( A e. On -> ( ~P A i^i On ) = suc A ) |