Theorem rphalfcl

Description: Closure law for half of a positive real. (Contributed by Mario Carneiro, 31-Jan-2014)

	Ref	Expression
Assertion	rphalfcl	$$⊢A\in {ℝ}^{+}\to \frac{A}{2}\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		2rp	$$⊢2\in {ℝ}^{+}$$
2		rpdivcl	$$⊢\left(A\in {ℝ}^{+}\wedge 2\in {ℝ}^{+}\right)\to \frac{A}{2}\in {ℝ}^{+}$$
3	1 2	mpan2	$$⊢A\in {ℝ}^{+}\to \frac{A}{2}\in {ℝ}^{+}$$