Theorem eluz3nn

Description: An integer greater than or equal to 3 is a positive integer. (Contributed by Alexander van der Vekens, 17-Sep-2018) (Proof shortened by AV, 30-Nov-2025)

	Ref	Expression
Assertion	eluz3nn	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 3 ) → 𝑁 ∈ ℕ )

Proof

Step	Hyp	Ref	Expression
1		uzuzle23	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 3 ) → 𝑁 ∈ ( ℤ≥ ‘ 2 ) )
2		eluz2nn	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 2 ) → 𝑁 ∈ ℕ )
3	1 2	syl	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 3 ) → 𝑁 ∈ ℕ )