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Metamath Proof Explorer

Theorem rphalfcl

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

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

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