Theorem orduniss

Description: An ordinal class includes its union. (Contributed by NM, 13-Sep-2003)

	Ref	Expression
Assertion	orduniss	⊢ ( Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ordtr	⊢ ( Ord 𝐴 → Tr 𝐴 )
2		df-tr	⊢ ( Tr 𝐴 ↔ ∪ 𝐴 ⊆ 𝐴 )
3	1 2	sylib	⊢ ( Ord 𝐴 → ∪ 𝐴 ⊆ 𝐴 )