Theorem gt0ne0ii

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

	Ref	Expression
Hypotheses	lt2.1	$$⊢A\in ℝ$$
	gt0ne0i.2	$$⊢0<A$$
Assertion	gt0ne0ii	$$⊢A\ne 0$$

Proof

Step	Hyp	Ref	Expression
1		lt2.1	$$⊢A\in ℝ$$
2		gt0ne0i.2	$$⊢0<A$$
3	1	gt0ne0i	$$⊢0<A\to A\ne 0$$
4	2 3	ax-mp	$$⊢A\ne 0$$