Theorem mulgt0i

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

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	mulgt0i	|- ( ( 0 < A /\ 0 < B ) -> 0 < ( A x. B ) )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		axmulgt0	|- ( ( A e. RR /\ B e. RR ) -> ( ( 0 < A /\ 0 < B ) -> 0 < ( A x. B ) ) )
4	1 2 3	mp2an	|- ( ( 0 < A /\ 0 < B ) -> 0 < ( A x. B ) )