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 )