Theorem rpreccld

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

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

Proof

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