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Metamath Proof Explorer

Theorem pion

Description: A positive integer is an ordinal number. (Contributed by NM, 23-Mar-1996) (New usage is discouraged.)

		Ref	Expression
	Assertion	pion	$⊢ A \in 𝑵 \to A \in On$

Step	Hyp	Ref	Expression
1		pinn	$⊢ A \in 𝑵 \to A \in ω$
2		nnon	$⊢ A \in ω \to A \in On$
3	1 2	syl	$⊢ A \in 𝑵 \to A \in On$