Theorem halfcl

Description: Closure of half of a number. (Contributed by NM, 1-Jan-2006)

	Ref	Expression
Assertion	halfcl	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 / 2 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		2cn	⊢ 2 ∈ ℂ
2		2ne0	⊢ 2 ≠ 0
3		divcl	⊢ ( ( 𝐴 ∈ ℂ ∧ 2 ∈ ℂ ∧ 2 ≠ 0 ) → ( 𝐴 / 2 ) ∈ ℂ )
4	1 2 3	mp3an23	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 / 2 ) ∈ ℂ )