Metamath Proof Explorer


Theorem rehalfcld

Description: Real closure of half. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis rehalfcld.1 ⊢ φ → A ∈ ℝ
Assertion rehalfcld ⊢ φ → A 2 ∈ ℝ

Proof

Step Hyp Ref Expression
1 rehalfcld.1 ⊢ φ → A ∈ ℝ
2 rehalfcl ⊢ A ∈ ℝ → A 2 ∈ ℝ
3 1 2 syl ⊢ φ → A 2 ∈ ℝ