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Metamath Proof Explorer

Theorem rpreccl

Description: Closure law for reciprocation of positive reals. (Contributed by Jeff Hankins, 23-Nov-2008)

		Ref	Expression
	Assertion	rpreccl	$⊢ A \in ℝ^{+} \to \frac{1}{A} \in ℝ^{+}$

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