Theorem rprege0

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

	Ref	Expression
Assertion	rprege0	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge 0\le A\right)$$

Proof

Step	Hyp	Ref	Expression
1		rpre	$$⊢A\in {ℝ}^{+}\to A\in ℝ$$
2		rpge0	$$⊢A\in {ℝ}^{+}\to 0\le A$$
3	1 2	jca	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge 0\le A\right)$$