Metamath Proof Explorer


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 ) )