Theorem rprege0

Description: A positive real is a nonnegative real number. (Contributed by Mario Carneiro, 31-Jan-2014)

	Ref	Expression
Assertion	rprege0	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		rpre	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )
2		rpge0	⊢ ( 𝐴 ∈ ℝ+ → 0 ≤ 𝐴 )
3	1 2	jca	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) )