Theorem halfcld

Description: Closure of half of a number (frequently used special case). (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	2timesd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
Assertion	halfcld	⊢ ( 𝜑 → ( 𝐴 / 2 ) ∈ ℂ )

Proof

Step	Hyp	Ref	Expression
1		2timesd.1	⊢ ( 𝜑 → 𝐴 ∈ ℂ )
2		halfcl	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 / 2 ) ∈ ℂ )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 / 2 ) ∈ ℂ )