Theorem mulgt0i

Description: The product of two positive numbers is positive. (Contributed by NM, 16-May-1999)

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
Assertion	mulgt0i	$$⊢\left(0<A\wedge 0<B\right)\to 0<AB$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3		axmulgt0	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left(\left(0<A\wedge 0<B\right)\to 0<AB\right)$$
4	1 2 3	mp2an	$$⊢\left(0<A\wedge 0<B\right)\to 0<AB$$