Theorem rerecclzi

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

	Ref	Expression
Hypothesis	redivcl.1	$$⊢A\in ℝ$$
Assertion	rerecclzi	$$⊢A\ne 0\to \frac{1}{A}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		redivcl.1	$$⊢A\in ℝ$$
2		rereccl	$$⊢\left(A\in ℝ\wedge A\ne 0\right)\to \frac{1}{A}\in ℝ$$
3	1 2	mpan	$$⊢A\ne 0\to \frac{1}{A}\in ℝ$$