Theorem elrpii

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

	Ref	Expression
Hypotheses	elrpi.1	⊢ 𝐴 ∈ ℝ
	elrpi.2	⊢ 0 < 𝐴
Assertion	elrpii	⊢ 𝐴 ∈ ℝ+

Proof

Step	Hyp	Ref	Expression
1		elrpi.1	⊢ 𝐴 ∈ ℝ
2		elrpi.2	⊢ 0 < 𝐴
3		elrp	⊢ ( 𝐴 ∈ ℝ+ ↔ ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) )
4	1 2 3	mpbir2an	⊢ 𝐴 ∈ ℝ+