Theorem gt0ne0ii

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

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	gt0ne0i.2	|- 0 < A
Assertion	gt0ne0ii	|- A =/= 0

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		gt0ne0i.2	|- 0 < A
3	1	gt0ne0i	|- ( 0 < A -> A =/= 0 )
4	2 3	ax-mp	|- A =/= 0