Theorem reccli

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

	Ref	Expression
Hypotheses	divclz.1	$$⊢A\in ℂ$$
	reccl.2	$$⊢A\ne 0$$
Assertion	reccli	$$⊢\frac{1}{A}\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		divclz.1	$$⊢A\in ℂ$$
2		reccl.2	$$⊢A\ne 0$$
3	1	recclzi	$$⊢A\ne 0\to \frac{1}{A}\in ℂ$$
4	2 3	ax-mp	$$⊢\frac{1}{A}\in ℂ$$