Theorem rphalfcl

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

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

Proof

Step	Hyp	Ref	Expression
1		2rp	⊢ 2 ∈ ℝ+
2		rpdivcl	⊢ ( ( 𝐴 ∈ ℝ+ ∧ 2 ∈ ℝ+ ) → ( 𝐴 / 2 ) ∈ ℝ+ )
3	1 2	mpan2	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 / 2 ) ∈ ℝ+ )