Description: Closure law for division of a real by a positive real. (Contributed by NM, 10-Nov-2008)
Ref | Expression | ||
---|---|---|---|
Assertion | rerpdivcl | |- ( ( A e. RR /\ B e. RR+ ) -> ( A / B ) e. RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rprene0 | |- ( B e. RR+ -> ( B e. RR /\ B =/= 0 ) ) |
|
2 | redivcl | |- ( ( A e. RR /\ B e. RR /\ B =/= 0 ) -> ( A / B ) e. RR ) |
|
3 | 2 | 3expb | |- ( ( A e. RR /\ ( B e. RR /\ B =/= 0 ) ) -> ( A / B ) e. RR ) |
4 | 1 3 | sylan2 | |- ( ( A e. RR /\ B e. RR+ ) -> ( A / B ) e. RR ) |