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 ∈ On → 𝐴 ⊆ On )

Proof

Step Hyp Ref Expression
1 eloni ( 𝐴 ∈ On → Ord 𝐴 )
2 ordsson ( Ord 𝐴𝐴 ⊆ On )
3 1 2 syl ( 𝐴 ∈ On → 𝐴 ⊆ On )