Theorem rerecclzi

Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)

	Ref	Expression
Hypothesis	redivcl.1	|- A e. RR
Assertion	rerecclzi	|- ( A =/= 0 -> ( 1 / A ) e. RR )

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	|- A e. RR
2		rereccl	|- ( ( A e. RR /\ A =/= 0 ) -> ( 1 / A ) e. RR )
3	1 2	mpan	|- ( A =/= 0 -> ( 1 / A ) e. RR )