Theorem rprecred

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	rprecred	$$⊢\phi \to \frac{1}{A}\in ℝ$$

Proof

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