Metamath Proof Explorer

Theorem rpreccl

Description: Closure law for reciprocation of positive reals. (Contributed by Jeff Hankins, 23-Nov-2008)

Ref Expression
Assertion rpreccl 
|- ( A e. RR+ -> ( 1 / A ) e. RR+ )

Proof

Step Hyp Ref Expression
1 1rp 
 |-  1 e. RR+
2 rpdivcl 
 |-  ( ( 1 e. RR+ /\ A e. RR+ ) -> ( 1 / A ) e. RR+ )
3 1 2 mpan 
 |-  ( A e. RR+ -> ( 1 / A ) e. RR+ )