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 ∈ On → ( 𝒫 𝐴 ∩ On ) = suc 𝐴 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni | ⊢ ( 𝐴 ∈ On → Ord 𝐴 ) | |
2 | ordpwsuc | ⊢ ( Ord 𝐴 → ( 𝒫 𝐴 ∩ On ) = suc 𝐴 ) | |
3 | 1 2 | syl | ⊢ ( 𝐴 ∈ On → ( 𝒫 𝐴 ∩ On ) = suc 𝐴 ) |