Theorem rpreccld

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

	Ref	Expression
Hypothesis	rpred.1	|- ( ph -> A e. RR+ )
Assertion	rpreccld	|- ( ph -> ( 1 / A ) e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	|- ( ph -> A e. RR+ )
2		rpreccl	|- ( A e. RR+ -> ( 1 / A ) e. RR+ )
3	1 2	syl	|- ( ph -> ( 1 / A ) e. RR+ )