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 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		elrp	⊢ ( 𝐴 ∈ ℝ+ ↔ ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) )
2	1	biimpi	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) )