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 ∈ On
Assertion	onunisuci	⊢ ∪ suc 𝐴 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		on.1	⊢ 𝐴 ∈ On
2		onunisuc	⊢ ( 𝐴 ∈ On → ∪ suc 𝐴 = 𝐴 )
3	1 2	ax-mp	⊢ ∪ suc 𝐴 = 𝐴