Theorem gt0ne0ii

Description: Positive implies nonzero. (Contributed by NM, 15-May-1999)

	Ref	Expression
Hypotheses	lt2.1	⊢ 𝐴 ∈ ℝ
	gt0ne0i.2	⊢ 0 < 𝐴
Assertion	gt0ne0ii	⊢ 𝐴 ≠ 0

Proof

Step	Hyp	Ref	Expression
1		lt2.1	⊢ 𝐴 ∈ ℝ
2		gt0ne0i.2	⊢ 0 < 𝐴
3	1	gt0ne0i	⊢ ( 0 < 𝐴 → 𝐴 ≠ 0 )
4	2 3	ax-mp	⊢ 𝐴 ≠ 0