Theorem reccl

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

	Ref	Expression
Assertion	reccl	$$⊢\left(A\in ℂ\wedge A\ne 0\right)\to \frac{1}{A}\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		ax-1cn	$$⊢1\in ℂ$$
2		divcl	$$⊢\left(1\in ℂ\wedge A\in ℂ\wedge A\ne 0\right)\to \frac{1}{A}\in ℂ$$
3	1 2	mp3an1	$$⊢\left(A\in ℂ\wedge A\ne 0\right)\to \frac{1}{A}\in ℂ$$