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 ∈ N → 𝐴 ∈ ω )

Proof

Step	Hyp	Ref	Expression
1		df-ni	⊢ N = ( ω ∖ { ∅ } )
2		difss	⊢ ( ω ∖ { ∅ } ) ⊆ ω
3	1 2	eqsstri	⊢ N ⊆ ω
4	3	sseli	⊢ ( 𝐴 ∈ N → 𝐴 ∈ ω )