Theorem mulgt0ii

Description: The product of two positive numbers is positive. (Contributed by NM, 18-May-1999)

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
	mulgt0i.3	$$⊢0<A$$
	mulgt0i.4	$$⊢0<B$$
Assertion	mulgt0ii	$$⊢0<AB$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3		mulgt0i.3	$$⊢0<A$$
4		mulgt0i.4	$$⊢0<B$$
5	1 2	mulgt0i	$$⊢\left(0<A\wedge 0<B\right)\to 0<AB$$
6	3 4 5	mp2an	$$⊢0<AB$$