Theorem rehalfcl

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

	Ref	Expression
Assertion	rehalfcl	$$⊢A\in ℝ\to \frac{A}{2}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		2re	$$⊢2\in ℝ$$
2		2ne0	$$⊢2\ne 0$$
3		redivcl	$$⊢\left(A\in ℝ\wedge 2\in ℝ\wedge 2\ne 0\right)\to \frac{A}{2}\in ℝ$$
4	1 2 3	mp3an23	$$⊢A\in ℝ\to \frac{A}{2}\in ℝ$$