Theorem rpdivcld

Description: Closure law for division of positive reals. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	rpred.1	|- ( ph -> A e. RR+ )
	rpaddcld.1	|- ( ph -> B e. RR+ )
Assertion	rpdivcld	|- ( ph -> ( A / B ) e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	|- ( ph -> A e. RR+ )
2		rpaddcld.1	|- ( ph -> B e. RR+ )
3		rpdivcl	|- ( ( A e. RR+ /\ B e. RR+ ) -> ( A / B ) e. RR+ )
4	1 2 3	syl2anc	|- ( ph -> ( A / B ) e. RR+ )