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 ∈ ℂ
	divclz.2	⊢ 𝐵 ∈ ℂ
	divcl.3	⊢ 𝐵 ≠ 0
Assertion	divcli	⊢ ( 𝐴 / 𝐵 ) ∈ ℂ

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		divclz.2	⊢ 𝐵 ∈ ℂ
3		divcl.3	⊢ 𝐵 ≠ 0
4	1 2	divclzi	⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℂ )
5	3 4	ax-mp	⊢ ( 𝐴 / 𝐵 ) ∈ ℂ