Theorem elnnuz

Description: A positive integer expressed as a member of an upper set of integers. (Contributed by NM, 6-Jun-2006)

	Ref	Expression
Assertion	elnnuz	⊢ ( 𝑁 ∈ ℕ ↔ 𝑁 ∈ ( ℤ≥ ‘ 1 ) )

Proof

Step	Hyp	Ref	Expression
1		nnuz	⊢ ℕ = ( ℤ≥ ‘ 1 )
2	1	eleq2i	⊢ ( 𝑁 ∈ ℕ ↔ 𝑁 ∈ ( ℤ≥ ‘ 1 ) )