Theorem eluz2nn

Description: An integer greater than or equal to 2 is a positive integer. (Contributed by AV, 3-Nov-2018)

	Ref	Expression
Assertion	eluz2nn	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) → 𝐴 ∈ ℕ )

Proof

Step	Hyp	Ref	Expression
1		1z	⊢ 1 ∈ ℤ
2		1le2	⊢ 1 ≤ 2
3		eluzuzle	⊢ ( ( 1 ∈ ℤ ∧ 1 ≤ 2 ) → ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) → 𝐴 ∈ ( ℤ≥ ‘ 1 ) ) )
4	1 2 3	mp2an	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) → 𝐴 ∈ ( ℤ≥ ‘ 1 ) )
5		nnuz	⊢ ℕ = ( ℤ≥ ‘ 1 )
6	4 5	eleqtrrdi	⊢ ( 𝐴 ∈ ( ℤ≥ ‘ 2 ) → 𝐴 ∈ ℕ )