Theorem mulgt0ii

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

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
	mulgt0i.3	|- 0 < A
	mulgt0i.4	|- 0 < B
Assertion	mulgt0ii	|- 0 < ( A x. B )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		mulgt0i.3	|- 0 < A
4		mulgt0i.4	|- 0 < B
5	1 2	mulgt0i	|- ( ( 0 < A /\ 0 < B ) -> 0 < ( A x. B ) )
6	3 4 5	mp2an	|- 0 < ( A x. B )