Theorem onunisuc

Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994) Generalize from onunisuci . (Revised by BJ, 28-Dec-2024)

	Ref	Expression
Assertion	onunisuc	|- ( A e. On -> U. suc A = A )

Proof

Step	Hyp	Ref	Expression
1		ontr	|- ( A e. On -> Tr A )
2		unisucg	|- ( A e. On -> ( Tr A <-> U. suc A = A ) )
3	1 2	mpbid	|- ( A e. On -> U. suc A = A )