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Metamath Proof Explorer

Theorem nnord

Description: A natural number is ordinal. (Contributed by NM, 17-Oct-1995)

		Ref	Expression
	Assertion	nnord	⊢ ( 𝐴 ∈ ω → Ord 𝐴 )

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