Theorem gt0ne0i

Description: Positive means nonzero (useful for ordering theorems involving division). (Contributed by NM, 16-Sep-1999)

	Ref	Expression
Hypothesis	lt2.1	⊢ 𝐴 ∈ ℝ
Assertion	gt0ne0i	⊢ ( 0 < 𝐴 → 𝐴 ≠ 0 )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	⊢ 𝐴 ∈ ℝ
2		0re	⊢ 0 ∈ ℝ
3	2 1	ltnei	⊢ ( 0 < 𝐴 → 𝐴 ≠ 0 )