Theorem pinn

Description: A positive integer is a natural number. (Contributed by NM, 15-Aug-1995) (New usage is discouraged.)

	Ref	Expression
Assertion	pinn	$$⊢A\in 𝑵\to A\in \mathrm{\omega }$$

Proof

Step	Hyp	Ref	Expression
1		df-ni	$$⊢𝑵=\mathrm{\omega }\setminus \left\{\varnothing \right\}$$
2		difss	$$⊢\mathrm{\omega }\setminus \left\{\varnothing \right\}\subseteq \mathrm{\omega }$$
3	1 2	eqsstri	$$⊢𝑵\subseteq \mathrm{\omega }$$
4	3	sseli	$$⊢A\in 𝑵\to A\in \mathrm{\omega }$$