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Metamath Proof Explorer

Theorem onss

Description: An ordinal number is a subset of the class of ordinal numbers. (Contributed by NM, 5-Jun-1994)

Ref Expression
Assertion onss 
|- ( A e. On -> A C_ On )

Proof

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