Theorem rprene0

Description: A positive real is a nonzero real number. (Contributed by NM, 11-Nov-2008)

	Ref	Expression
Assertion	rprene0	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge A\ne 0\right)$$

Proof

Step	Hyp	Ref	Expression
1		rpre	$$⊢A\in {ℝ}^{+}\to A\in ℝ$$
2		rpne0	$$⊢A\in {ℝ}^{+}\to A\ne 0$$
3	1 2	jca	$$⊢A\in {ℝ}^{+}\to \left(A\in ℝ\wedge A\ne 0\right)$$