Metamath Proof Explorer

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 C_ suc U. A )

Proof

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