Theorem nnne0i

Description: A positive integer is nonzero (inference version). (Contributed by NM, 25-Aug-1999)

	Ref	Expression
Hypothesis	nngt0.1	⊢ 𝐴 ∈ ℕ
Assertion	nnne0i	⊢ 𝐴 ≠ 0

Proof

Step	Hyp	Ref	Expression
1		nngt0.1	⊢ 𝐴 ∈ ℕ
2	1	nnrei	⊢ 𝐴 ∈ ℝ
3	1	nngt0i	⊢ 0 < 𝐴
4	2 3	gt0ne0ii	⊢ 𝐴 ≠ 0