Theorem rehalfcl

Description: Real closure of half. (Contributed by NM, 1-Jan-2006)

	Ref	Expression
Assertion	rehalfcl	⊢ ( 𝐴 ∈ ℝ → ( 𝐴 / 2 ) ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		2re	⊢ 2 ∈ ℝ
2		2ne0	⊢ 2 ≠ 0
3		redivcl	⊢ ( ( 𝐴 ∈ ℝ ∧ 2 ∈ ℝ ∧ 2 ≠ 0 ) → ( 𝐴 / 2 ) ∈ ℝ )
4	1 2 3	mp3an23	⊢ ( 𝐴 ∈ ℝ → ( 𝐴 / 2 ) ∈ ℝ )