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 )