Theorem rphalfcld

Description: Closure law for half of a positive real. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	rphalfcld	⊢ ( 𝜑 → ( 𝐴 / 2 ) ∈ ℝ+ )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		rphalfcl	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 / 2 ) ∈ ℝ+ )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 / 2 ) ∈ ℝ+ )