Metamath Proof Explorer


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+ )