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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 ∈ On → 𝐴 ⊆ On )

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