Theorem recgt0i

Description: The reciprocal of a positive number is positive. Exercise 4 of Apostol p. 21. (Contributed by NM, 15-May-1999)

	Ref	Expression
Hypothesis	ltplus1.1	$$⊢A\in ℝ$$
Assertion	recgt0i	$$⊢0<A\to 0<\frac{1}{A}$$

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	$$⊢A\in ℝ$$
2		recgt0	$$⊢\left(A\in ℝ\wedge 0<A\right)\to 0<\frac{1}{A}$$
3	1 2	mpan	$$⊢0<A\to 0<\frac{1}{A}$$