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+ ) |
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+ ) |