Theorem ordsucuni

Description: An ordinal class is a subclass of the successor of its union. (Contributed by NM, 12-Sep-2003)

	Ref	Expression
Assertion	ordsucuni	⊢ ( Ord 𝐴 → 𝐴 ⊆ suc ∪ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ordsson	⊢ ( Ord 𝐴 → 𝐴 ⊆ On )
2		onsucuni	⊢ ( 𝐴 ⊆ On → 𝐴 ⊆ suc ∪ 𝐴 )
3	1 2	syl	⊢ ( Ord 𝐴 → 𝐴 ⊆ suc ∪ 𝐴 )