Theorem divclzi

Description: Closure law for division. (Contributed by NM, 7-May-1999) (Revised by Mario Carneiro, 17-Feb-2014)

	Ref	Expression
Hypotheses	divclz.1	⊢ 𝐴 ∈ ℂ
	divclz.2	⊢ 𝐵 ∈ ℂ
Assertion	divclzi	⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		divclz.1	⊢ 𝐴 ∈ ℂ
2		divclz.2	⊢ 𝐵 ∈ ℂ
3		divcl	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ∧ 𝐵 ≠ 0 ) → ( 𝐴 / 𝐵 ) ∈ ℂ )
4	1 2 3	mp3an12	⊢ ( 𝐵 ≠ 0 → ( 𝐴 / 𝐵 ) ∈ ℂ )