Metamath Proof Explorer


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