Theorem divcli

Description: Closure law for division. (Contributed by NM, 2-Feb-1995) (Revised by Mario Carneiro, 17-Feb-2014)

	Ref	Expression
Hypotheses	divclz.1	$$⊢A\in ℂ$$
	divclz.2	$$⊢B\in ℂ$$
	divcl.3	$$⊢B\ne 0$$
Assertion	divcli	$$⊢\frac{A}{B}\in ℂ$$

Proof

Step	Hyp	Ref	Expression
1		divclz.1	$$⊢A\in ℂ$$
2		divclz.2	$$⊢B\in ℂ$$
3		divcl.3	$$⊢B\ne 0$$
4	1 2	divclzi	$$⊢B\ne 0\to \frac{A}{B}\in ℂ$$
5	3 4	ax-mp	$$⊢\frac{A}{B}\in ℂ$$