Theorem elrpii

Description: Membership in the set of positive reals. (Contributed by NM, 23-Feb-2008)

	Ref	Expression
Hypotheses	elrpi.1	$$⊢A\in ℝ$$
	elrpi.2	$$⊢0<A$$
Assertion	elrpii	$$⊢A\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		elrpi.1	$$⊢A\in ℝ$$
2		elrpi.2	$$⊢0<A$$
3		elrp	$$⊢A\in {ℝ}^{+}\leftrightarrow \left(A\in ℝ\wedge 0<A\right)$$
4	1 2 3	mpbir2an	$$⊢A\in {ℝ}^{+}$$