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Metamath Proof Explorer

Theorem onpwsuc

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	$⊢ A \in On \to 𝒫 A \cap On = suc A$

Step	Hyp	Ref	Expression
1		eloni	$⊢ A \in On \to Ord A$
2		ordpwsuc	$⊢ Ord A \to 𝒫 A \cap On = suc A$
3	1 2	syl	$⊢ A \in On \to 𝒫 A \cap On = suc A$