Theorem eluz5nn

Description: An integer greater than or equal to 5 is a positive integer. (Contributed by AV, 22-Nov-2025)

	Ref	Expression
Assertion	eluz5nn	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 5 ) → 𝑁 ∈ ℕ )

Proof

Step	Hyp	Ref	Expression
1		uzuzle35	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 5 ) → 𝑁 ∈ ( ℤ≥ ‘ 3 ) )
2		eluz3nn	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 3 ) → 𝑁 ∈ ℕ )
3	1 2	syl	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 5 ) → 𝑁 ∈ ℕ )