Theorem pion

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

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

Proof

Step	Hyp	Ref	Expression
1		pinn	$$⊢A\in 𝑵\to A\in \mathrm{\omega }$$
2		nnon	$$⊢A\in \mathrm{\omega }\to A\in \mathrm{On}$$
3	1 2	syl	$$⊢A\in 𝑵\to A\in \mathrm{On}$$