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Metamath Proof Explorer

Theorem rpgt0

Description: A positive real is greater than zero. (Contributed by FL, 27-Dec-2007)

Ref Expression
Assertion rpgt0 ( 𝐴 ∈ ℝ+ → 0 < 𝐴 )

Proof

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