Theorem rpgt0d

Description: A positive real is greater than zero. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	rpgt0d	⊢ ( 𝜑 → 0 < 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		rpred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2		rpgt0	⊢ ( 𝐴 ∈ ℝ+ → 0 < 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → 0 < 𝐴 )