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Metamath Proof Explorer

Theorem onunisuci

Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994)

		Ref	Expression
	Hypothesis	on.1	$⊢ A \in On$
	Assertion	onunisuci	$⊢ ⋃ suc A = A$

Step	Hyp	Ref	Expression
1		on.1	$⊢ A \in On$
2		onunisuc	$⊢ A \in On \to ⋃ suc A = A$
3	1 2	ax-mp	$⊢ ⋃ suc A = A$