Theorem rpregt0

Description: A positive real is a positive real number. (Contributed by NM, 11-Nov-2008) (Revised by Mario Carneiro, 31-Jan-2014)

	Ref	Expression
Assertion	rpregt0	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge 0<A\right)$$

Proof

Step	Hyp	Ref	Expression
1		elrp	$$⊢A\in {ℝ}^{+}\leftrightarrow \left(A\in ℝ\wedge 0<A\right)$$
2	1	biimpi	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge 0<A\right)$$