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Metamath Proof Explorer

Theorem rpreccld

Description: Closure law for reciprocation of positive reals. (Contributed by Mario Carneiro, 28-May-2016)

		Ref	Expression
	Hypothesis	rpred.1	$⊢ φ \to A \in ℝ^{+}$
	Assertion	rpreccld	$⊢ φ \to \frac{1}{A} \in ℝ^{+}$

Step	Hyp	Ref	Expression
1		rpred.1	$⊢ φ \to A \in ℝ^{+}$
2		rpreccl	$⊢ A \in ℝ^{+} \to \frac{1}{A} \in ℝ^{+}$
3	1 2	syl	$⊢ φ \to \frac{1}{A} \in ℝ^{+}$