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 U. A )

Proof

Step Hyp Ref Expression
1 ordsson 
 |-  ( Ord A -> A C_ On )
2 ssorduni 
 |-  ( A C_ On -> Ord U. A )
3 1 2 syl 
 |-  ( Ord A -> Ord U. A )