Theorem mulge0i

Description: The product of two nonnegative numbers is nonnegative. (Contributed by NM, 30-Jul-1999)

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	lt2.2	|- B e. RR
Assertion	mulge0i	|- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A x. B ) )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		lt2.2	|- B e. RR
3		mulge0	|- ( ( ( A e. RR /\ 0 <_ A ) /\ ( B e. RR /\ 0 <_ B ) ) -> 0 <_ ( A x. B ) )
4	3	an4s	|- ( ( ( A e. RR /\ B e. RR ) /\ ( 0 <_ A /\ 0 <_ B ) ) -> 0 <_ ( A x. B ) )
5	1 2 4	mpanl12	|- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A x. B ) )