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 ∈ On → ∪ suc 𝐴 = 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ontr	⊢ ( 𝐴 ∈ On → Tr 𝐴 )
2		unisucg	⊢ ( 𝐴 ∈ On → ( Tr 𝐴 ↔ ∪ suc 𝐴 = 𝐴 ) )
3	1 2	mpbid	⊢ ( 𝐴 ∈ On → ∪ suc 𝐴 = 𝐴 )