Metamath Proof Explorer


Theorem orduni

Description: The union of an ordinal class is ordinal. (Contributed by NM, 12-Sep-2003)

Ref Expression
Assertion orduni ( Ord 𝐴 → Ord ∪ 𝐴 )

Proof

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