Theorem recclzi

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

	Ref	Expression
Hypothesis	divclz.1	$$⊢A\in ℂ$$
Assertion	recclzi	$$⊢A\ne 0\to \frac{1}{A}\in ℂ$$

Proof

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