Theorem prodgt0i

Description: Infer that a multiplicand is positive from a nonnegative multiplier and positive product. (Contributed by NM, 15-May-1999)

	Ref	Expression
Hypotheses	ltplus1.1	|- A e. RR
	prodgt0.2	|- B e. RR
Assertion	prodgt0i	|- ( ( 0 <_ A /\ 0 < ( A x. B ) ) -> 0 < B )

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	|- A e. RR
2		prodgt0.2	|- B e. RR
3		prodgt0	|- ( ( ( A e. RR /\ B e. RR ) /\ ( 0 <_ A /\ 0 < ( A x. B ) ) ) -> 0 < B )
4	1 2 3	mpanl12	|- ( ( 0 <_ A /\ 0 < ( A x. B ) ) -> 0 < B )